It's kind of in the definition of what 1 is to say that 1 to the power of anything is 1. You can use complicated powers, but the outcome will always be 1.
How do you calculate n's power?The simplest method for determining a number's nth power is to multiply it exactly n times. In this situation, we might simply calculate pow(2,-3) = 1/(23), which is the inverse of its positive power.
How is 1 n solved?Divide both sides by the left-hand integer to create a ratio with the notation 1: n. Divide both sides by the right-hand integer to represent the ratio as n: 1. to check if you're right.
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A 60kg man standing on a stationary 4okg boat throws a 0.2kg ball with a velocity of 50 m/s. Assuming there is no friction between the man and the boat, what is the speed of the boat after the man throws the ball?
Answer:
5/32 or 0.16 m/s
Explanation:
m1u1 + m2u2 = m1v1 + m2v2
(64x0) + (0.2 x 0) = (64 x v1) + (0.2 x 50)
v = (0.2 x 50) / 64
v = 5/32 or 0.16 m/s
(ignore negative sign as it means that the boat is moving the opposite direction of ball, that's why the answer was coming negative)
I hope my answer helps you.
What percent remains after 2 half-lives?
25 % This table shows that the amount of reactant remaining following n first-order reaction half-lives is (1/2)n times the initial concentration.
How much of a radioisotope sample is still present after two half-lives?As a result, 50% of the original parent nuclei are still present after one half-life, 25% after two half-lives, etc. The half-life and the initial quantity of radioactive atoms present both affect how much radiation is produced by a radioactive source.
After two half-lives, what is the daughter parent ratio?Therefore, after two half-lives, the parent-to-daughter atom ratio is 1:3. (one-quarter to three-quarters). The original parent is reduced to an eighth, a sixteenth, a thirty-second, and so on via successive half-lives.
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Which excerpt is an example of situational irony in sake's the storyteller?
“Most of the aunt’s remarks seemed to begin with ‘Don’t,’ and nearly all of the children’s remarks began with ‘Why?’ The bachelor said nothing out loud. ‘Don’t, Cyril, don’t,’ exclaimed the aunt, as the small boy began smacking the cushions of the seat, producing a cloud of dust at each blow.”
This statement is the correct answer for it.
It is taken from The story-teller, written by Saki.
What is situational irony?Situational irony is the irony of something happening that is very different to what was expected.
Irony involves a situation in which actions have an effect that is opposite from what was intended, so that the outcome is contrary to what was expected.
Situational irony involves the result of a situation not matching with your expectations, such as a baker being allergic to flour.
Situational irony allows writers to show the characters' intentions versus the outcomes, appearance versus reality.
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What is the wavelength answer?
Wavelength is basically the distance between two successive crests or troughs in a wave.
What are Crests?
Crests are points on a wave where the amplitude is at a maximum. In physics, they are used to describe the shape of a wave, and the amplitude of the wave is measured from the crest to the trough.
Wavelength is typically measured in meters (m) or nanometers (nm). Wavelength is an important parameter in wave mechanics and is related to the frequency of the wave and its speed. Wavelength is inversely proportional to frequency, meaning that as frequency increases, wavelength decreases.
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What is reinforcement in Psychology?
Reinforcement can be positive, meaning that a desirable consequence is provided, or negative, meaning that an undesirable consequence is removed
Reinforcement in psychology is an important tool for motivating behavior. It works by providing a consequence after a behavior occurs that makes it more likely to happen again in similar situations. Positive reinforcement is providing a desirable consequence, such as praise or a reward, after a behavior. Negative reinforcement is the removal of an undesirable consequence, such as a punishment, after a behavior. Reinforcement can be used to shape and strengthen desirable behaviors, as well as decrease undesirable behaviors. It is an effective way of motivating people and can be used in a variety of different contexts.
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Give an example of each of the following energy conversions/transformations:
a. Electrical to heat
b. Chemical to heat
c. Electrical to mechanical
Please respond in 1–2 complete sentences for each item using your best grammar.
The example of each of the energy electrical to heat, chemical to heat, electrical to mechanical energy is as given below.
a.) Every electric heater has a resistor as its heating element. Electric heating is the conversion of electrical energy to thermal energy. It converts electrical energy into heat energy when an electric current crosses a resistor, according to the Joule heating principle.
b.) Exothermic reactions, which commonly release chemical energy in the form of heat, are those that take place. Newly formed bonds can store some of the heat energy required for a reaction to proceed as chemical energy.
c.) An electric motor converts electrical energy into mechanical energy. A generator converts mechanical energy into electrical energy. A storage dam's mechanical energy is transformed into electrical energy via a hydroelectric powerplant.
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1. Two projectiles are thrown from the same point with the same velocity of 50 ms‐¹. The first is projected Making at an angle of θ with the horizontal and the second with an angular of (90-θ)⁰. if the second is found to rise 25m higher than the first.
A. calculate the highest to which each will rise .
B. calculate and compare their range .
C. which one reaches the ground first
The highest to which the first projectile rises will be equal to 51.25 m and the second projectile is 76.29 m.
What is Projectile Motion?A projectile can be defined as an object that will be thrown obliquely near the surface, it follows along a curved path with constant acceleration.
In a Projectile Motion, along the y-axis, there is a constant acceleration, responsible for the vertical motion of the particle while along the x-axis plotted is uniform velocity, responsible for the horizontal motion.
The maximum height of the first projectile is given by:
[tex]\displaystyle Y_1 = \frac{u^2sin^2\theta}{2g}[/tex]
The maximum height of the second projectile is given by:
[tex]\displaystyle Y_2 = \frac{u^2sin^2(90-\theta)}{2g}[/tex]
[tex]\displaystyle Y_2 = \frac{u^2cos^2\theta}{2g}[/tex]
[tex]\displaystyle Y_2 -Y_1 = \frac{u^2(cos^2-sin^2\theta)}{2g}[/tex]
[tex]\displaystyle Y_2 -Y_1= \frac{u^2cos2\theta}{2g}[/tex]
Given, height difference Y₂ - Y₁ = 25 m, initial velocity, u = 50m/s
[tex]\displaystyle 25 = \frac{(50)^2cos2\theta}{2\times 9.8}[/tex]
cos 2θ = 0.196
θ = 39.34°
[tex]\displaystyle Y_1 = \frac{(50)^2sin^2 (39.34)}{2\times 9.8}[/tex]
Y₁ = 51.25 m
[tex]\displaystyle Y_2 = \frac{(50)^2sin^2 (50.66)}{2\times 9.8}[/tex]
Y₂ = 76.29 m
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what does the number 2.001 represent in the following: t(58) = 2.001, p < .05?
The degree of freedom in the equation is denoted by the number 58: t(58)=2.001, p.05.
The degree of freedom refers to how many logically independent value i.e., values with the freedom to change there are in the sample of data. One is deducted from the total number of elements in the data sample when calculating degrees of freedom.
Degrees of freedom can be calculated using a simple statistical technique. Degrees of freedom are equal to the number of values in a data collection less one, as stated by the formula: df = N-1.
N is the total number of values included in this data collection (sample size).
The degrees of freedom, or the quantity of unrestricted data points available for comparison in a t-test The number 58 in the t-test above indicates the degrees of freedom, or the number of unrestricted data points available in a t-test to compare two groups.
(In statistics, a T-test is used to compare the means of two groups. The values required for a t test are the t-value, p-value, and degrees of freedom.)
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The wave oscillation period is 0.5 minutes. Find the length of this wave if its speed is 54 km/h
To find the length of the wave if its speed is 54 km/h, we can use the formula:
Wavelength = Speed / Frequency
where the frequency of the wave is equal to the inverse of the oscillation period. The oscillation period of the wave is 0.5 minutes, so the frequency is 1 / (0.5 minutes) = 2 oscillations/minute.
We can now plug these values into the formula to find the wavelength:
Wavelength = 54 km/h / (2 oscillations/minute)
= 27 km
Therefore, the length of the wave is 27 km
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What are the 4 types of reinforcement?
The four types of reinforcement include- positive reinforcement, negative reinforcement, punishment, extinction.
Positive reinforcement: Positive reinforcement is especially effective at establishing new behaviors, but it may not work as well in the long term if the subject becomes bored with the reward over time. This involves adding something to increase response, such as praising a child when they complete a designated task.
Negative reinforcement: Namely, negative in this theory means removing or subtracting something that either discourages negative behavior (punishment) or removes adverse stimuli to support or encourage certain behavior (reinforcement). This involves removing something to increase response, such as withholding payment until the person completes the job. The person would remain motivated till the end of the job to acquire the payment.
Punishment: Punishment is often mistakenly confused with negative reinforcement. Remember, reinforcement always increases the chances that a behavior will occur and punishment always decreases the chances that a behavior will occur. This involves adding something aversive to modify behavior. For example, yelling at a child for misbehaving. In this example, the child would associate every negative behavior with punishments. This would prevent the child from repeating such behavior.
Extinction: This involves removing or taking away something to modify a certain response. This is called negative punishment or extinction. For instance, a teenager comes home late, and the parents curb their phone usage. Next time, the teenager would think before breaking the curfew.
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a 200 g steel ball a hangs on a 1.0 m long string. the ball a is pulled sideways so that the string is at a 45-degree angle, then released. at the very bottom of its swing, the ball strikes a 500 g steel paperweight b that is resting on a frictionless table. to what angle does the ball rebound?
After solving the equation the ball rebound is θ2 = 18.88° is the correct answer.
What is Potential energy?
Potential energy is the energy held by an object due to its position or composition. It is the energy of an object that is stored and waiting to be released. This energy is due to the force of gravity, electric charge, and/or the force of a spring. Potential energy is also known as “stored energy”. It is measured in units of joules (J). Potential energy can be converted into kinetic energy, which is the energy of motion. Examples of potential energy include the energy stored in a stretched rubber band, the energy stored in a roller coaster car at the top of the hill, and the energy stored in a boulder at the top of a mountain. Potential energy can also be found in chemical bonds and nuclear energy.
Here Potential energy will convert to Kinetic energy,
P.E. (initial) + K.E. (initial) = P.E. (Final) + K.E. (Final)
M g L (1 – Cos 45) + 0 = 0 + ½ mv2
v2 = 2gL (1 – 1/0.414)
v = (2* 9.8* 1)0.5 * (1 – 1/0.414)0.5
v = 2.396 m/s
Thus, when ball strikes its velocity is 2.396 m/s.
From conservation of momentum
M1v1 + m2v2 = m1V1 + m2V2
0.2*2.396 = 0.2 V1 + 0.5 V2
Here, since no information is given for collision.
I am considering it to be elastic,
U1 – U2 = V2 – V1
U1 = V2 -V1
V2 – V1 = 2.396
0.2V1 + 0.5V2 = 0.4792
V1 = -1.027 m/s ; V2 = 1.369 m/s
i.e.,
½ m1v12 = m g L (1-Cos θ2) ---- Energy Conversion
V12 = 9.8 * 2 * 1 (1- Cos θ2)
1.055 = 19.6 (1 - Cos θ2)
Cos θ2 = 0.9462
θ2 = 18.88 °
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The diagram is an illustration of global atmospheric circulation. Which of the following is the source of energy driving the circulation pattern labeled C in the diagram?
answer choices
The Coriolis effect
Solar radiation
Earth's magnetic field
The spinning core of Earth
Solar radiation is labelled as C in the diagram of global atmospheric circulation.
Winds are created by global atmospheric circulation, which results to areas of significant rainfall, such as tropical rainforests, and areas of dry air, such as deserts.
The global atmospheric circulation model is a simplified representation of the movement of air currents in the atmosphere. It is employed to aid in the explanation of weather patterns and climatic zones. Cells serve as the foundation of the global atmospheric circulation model. These cells are areas where air travels from low to high pressure.
Even though weather fronts and storms cause interruptions, there is a continuous pattern to how air travels about our planet's atmosphere. Because the Sun heats the Earth more at the equator than at the poles, this pattern is known as atmospheric circulation. It is also influenced by earth rotatory.
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A bullet of mass 0.01kg is fired with velocity of [230,0]m/s in to a sack of sand of mass 9.99kg which is swinging from rope. At the moment the bullet hits, the sack has a velocity of [0,0.2]m/s. Workout the velocity of bullet of the sack.
Answer:
The velocity of the bullet and the sack after the bullet hits the sack is [0.2,0.2] m/s.
Explanation:
To calculate the velocity of the bullet and the sack after the bullet hits the sack, we can use the equation:
vf = (m1 * v1 + m2 * v2) / (m1 + m2)
Plugging in the values given in the question, we get:
vf = (0.01 kg * [230,0] m/s + 9.99 kg * [0,0.2] m/s) / (0.01 kg + 9.99 kg)
Solving for vf, we get:
vf = [0.2, 0.2] m/s
Therefore, the velocity of the bullet and the sack after the bullet hits the sack is [0.2,0.2] m/s.
The initial and final momentum of a body will be conserved during collision. From this concept, the final velocity of the bullet and sack is 2.5 m/s.
What is momentum?Momentum is the product of mass and velocity of a body. During a collision of two bodies, the sum of initial momentum of the two bodies will be equal to the sum of their final momentum.
Given that, mass of bullet = 0.01 Kg
velocity = 2300 m/s
mass of sand sack = 9.99 Kg
velocity = 0.2 m/s
Then sum of initial momentum = (0.01 kg × 2300 m/s) + (9.99 kg × 0.2 m/s) = 24.9 kg m/s.
The final momentum of the combined mass = (9.99 kg + 0.01 kg) v = 24.9 Kg m/s
Thus, final velocity v = 24.9 / ( (9.99 kg + 0.01 kg) = 2.5 m/s
Therefore, the velocity of the bullet and sack after the collision will be 2.5 m/s.
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someone pls help me solve this problem thank you!
1. The equation of trajectory is: y = 5x²/4 +2x; it is equation of parabola.
2. The position vector = 2ti + (5t² +4t) j
3. The position of point M at t = 3 s is: ( 6,57).
4. The magnitude of velocity of point M at any time t is 2√(25t²+20t+5).
5. The magnitude of acceleration is 10m/s².
What is velocity?The term velocity has been defined as the rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is known as a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Coordinates at any instant t are:
x = 2t; y = 5t² +4t
1. equation of trajectory is:
y = 5x²/4 +2x; it is equation of parabola.
2. position vector = 2ti + (5t² +4t) j
3. the position of point M at t = 3 s is: x = 2×3 = 6; y = 5×3² +4×3 = 57; i.e., ( 6,57)
4. the velocity vector of point M at any time t is = 2i + ( 10t +4) j
magnitude of velocity = √( 2² + (10t +4)² = 2√(25t²+20t+5).
5. the acceleration vector is = 10j m/s²
Therefore, its magnitude is =10m/s².
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What is the name for this timeboxed iteration?
Scrum teams typically use brief iterations to get fast feedback from a variety of customers at a particular time.
This time-boxed iteration is referred to in Scrum as a Sprint, and it typically lasts one week. A timeboxed iteration is a time-restricted period during which the team concentrates on a single objective and creates a new piece of software. This is a sprint in the Scrum methodology where the team works toward the sprint goal specified in the sprint planning. A timebox is a set amount of time during which a person or a team works to achieve a common objective. Timeboxing is a tool used in agile project management to keep work moving quickly and on schedule. It is also an important part of Scrum.
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What is the list order of accuracy for the second derivative Mcq?
The least possible order of accuracy for the second derivatives is 2.
What are derivatives?
A derivative is a security with a price that is dependent on or derived from one or more underlying assets. A derivative itself is a contract between two or more parties based on an asset or assets. Its value is determined by the fluctuations of the underlying asset. The common underlying assets include shares, bonds, commodities, currencies,. Interest rates and market indices.Derivatives can be traded (over-the-counter, OTC) or on an exchange. OTC derivatives make up a larger proportion of existing derivatives and are unregulated, while exchange-traded derivatives are standardizedTo know more about derivatives, click the link given below:
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How much power is required for an 80kg firefighter to run up 21.5m in 60s?
The amount of power required for the firefighter to run up the stairs in 60s is 28.66 watts
What is power?Power is described as the amount of energy transferred or converted per unit time.
parameters given ate
mass= 80kg
distance = 60seconds
We need to calculate the distance over which the force is applied. In this case, the firefighter is running up a 21.5m flight of stairs, so the distance is 21.5m.
Then, we calculate the amount of work required, we use the formula
Work done = Force* distance
Work done = 80kg * 21.5m = 1720 Newton
Therefore power = work done/ time
= 1720/ 60
Power = 28.66 watts
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What does an ammeter measure?
An ammeter is a device used to measure electric current in amperes, either in direct current (DC) or alternating current (AC).
Ammeters measure current in what ways?
A shunt resistor is used in digital ammeter systems to create a calibrated voltage proportionate to the current flowing. The analog-to-digital converter (ADC) in a digital voltmeter is then used to measure this voltage; the digital display is calibrated to show the current flowing through the shunt.
What three purposes does an ammeter serve?
1. It is utilise to gauge circuit current.
2. It is utilised in circuits to determine whether or not they are functioning properly.
3. It is also used in the electronic industry to examine the circuit and usage of the appliances.
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At what value of x does f have a discontinuity due to a vertical asymptote? give a reason for your answer.
If f has a discontinuity due to a vertical asymptote at x=a, then the function has a vertical asymptote at x=a.
A vertical asymptote occurs when the function approaches infinity as x approaches a certain value from either direction. This means that the function becomes arbitrarily large as x approaches the value of the vertical asymptote, but it never actually reaches the asymptote itself.
To determine the value of x at which f has a discontinuity due to a vertical asymptote, you need to find the value of x at which the function approaches infinity. This can often be done by examining the function and looking for expressions of the form 1/0 or 0/0, which indicate that the function is becoming infinitely large as x approaches a certain value.
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How do you solve a line cut by a transversal?
To solve a line cut by a transversal, use the properties of parallel lines, such as corresponding angles and alternate interior angles, to find the unknown angle measurements.
When a line is cut by a transversal, a number of simultaneous equations can be formed by using the properties of parallel lines. For example, the corresponding angles of the lines will always be equal, the alternate interior angles will be equal, and the consecutive interior angles will add up to 180 degrees. Using these properties, you can identify the unknown angle measurements. For example, if the measure of one of the corresponding angles is known, the measure of the other corresponding angle can be determined simply by using the fact that they are equal. Similarly, if one of the alternate interior angles is known, the other can be determined using the fact that they are equal. By forming these equations, you can solve for the unknown angle measurements.
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how would you rearrange the ideal gas equation to calculate the pressure of a gas multiply p by v divide nrt by v multiply nrt by v divide v by nrt multiply pv by rt
An ideal gas equation to calculate the pressure of a gas is PV=nRT where P is pressure, V is volume, n is number of mole,R is gas constant and T is temperature.
In thermodynamics, Ideal gas equation is a clear cut guess of the way of behaving of many gases under different circumstances. Ideal Gas Condition is the blend of experimental regulations like Charle's regulation, Boyle's regulation, Gay-Lussac's regulation, and Avogadro's regulation. Ideal Gas equation is the equation characterizing the conditions of the speculative gases communicated numerically by the blends of observational and actual constants. It is likewise called the general gas condition. It very well may be characterized as:
Ideal Gas equation is the equation characterizing the equations of the speculative gases communicated numerically by the blends of exact and actual constants. It is additionally called the general gas equation. It tends to be characterized as PV=nRT.
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If the mass of the bar is 50kg, and Shelbi exerts 550N of force, what is the acceleration of the bar?
If the mass of the bar is 50kg, and Shelbi exerts 550N of force, the acceleration of the bar is 11 N/m².
Describe force.A push, pull, or hit on any object that causes a change in its state of motion is referred to as applying force. One thing experiences a force from another. For instance, we can say that when a force was applied to the box in the form of a push, it changed its state from rest to motion because when a box is pushed, it goes forward and changes its state of motion.
Describe acceleration.Accelerations are vector quantities. According to Newton's Second Law, an object's acceleration is the result of two factors working together: the object's mass, which varies depending on the materials it is made of, and the net balance of all external forces acting on it.
Briefing:Acceleration= Force/Mass =550/50 = 11m/s²
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how many neutrinos per second should be incident on every square meter of the earth from this process? this huge number is indicative of how rarely a neutrino interacts, since large detectors observe very few per day.
The area is 4 times 1.496 times 10 to 11 meters squared, and when we divide this by the total amount of neutrinos created during the proton-proton cycle each second, we obtain 6 times 10 to 14 neutrinos per square meter every second on Earth.
At the distance from the earth, how many neutrinos flow through each square meter of a sphere's surface?Neutrinos carry away around 3% of the energy produced by nuclear fusion in the Sun. Scientists estimate about 35 million billion (3.5 1016) solar neutrinos pass through each square meter of the Earth's surface per second as a result of protons reacting and creating neutrinos inside the Sun's core.
Your thumbnail receives how many neutrinos each second?Your thumbnail receives about 100 billion solar neutrinos each second. Nuclear fusion occurs in the sun, where it results in the creation of neutrinos.
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All of the following are examples of heat conduction except
a pressing a shirt with a hot iron.
b warming your hands over a campfire.
C warming your hands by holding a cup of hot
chocolate.
d heating soup in a pan on a stovetop.
Answer:
b
Explanation:
warming your hands over a campfire is not a example of it conduction because in heat conduction the body which transverse heat into the other bodies should be connected physically in the case of farming our hands over campfire there is no solid connectors our hands are being heated due to the radiation from the camp fire
Some microwaves operate using 1100 W of electrical power. If the current in the outlet is 20 A, what voltage is needed?
The voltage needed is 55 Volt.
What is electric power?
The rate at which energy is converted into an electrical circuit or used to produce work is known as electric power. It is a way to quantify how much energy is consumed over a certain period of time.
Given that: the microwaves operate using 1100 W of electrical power and the current in the outlet is 20 A,
Let, voltage needed is V.
We know that: electric power = voltage*current
Hence, Electric voltage = power / currect
= 1100 W/20 A
= 55 Volt.
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heather and jerry are standing on a bridge 51 m above a river. heather throws a rock straight down with a speed of 17 m/s . jerry, at exactly the same instant of time, throws a rock straight up with the same speed. ignore air resistance. part a how much time elapses between the first splash and the second splash? express your answer to two significant figures and include the appropriate units.
Jerry launches his rock upward at a speed of 20 m/s. It will slow down until its velocity hits zero at a rate of 9.8 m/s2. At that point, it will have reached apogee and will start to plummet. Therefore, 20 m/(9.8 m/s) = 2.04 seconds. to your maximum height.
After 2.04 seconds, it will start to accelerate downward once more, this time by 9.8 m/s2. Therefore, it will arrive at the starting place after an additional 2.04 seconds while moving at 20 m/s. Then it will travel through time in a similar manner to Heather's rock.
Jerry's pebble will therefore impact the sea 4.08 seconds later than Heather's. For this issue, it is not important to know how high you are above the sea.
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A rocket, initially at rest on the ground, accelerates straight upward from rest with constant (net) acceleration 58.8 m/s^2 . The acceleration period lasts for time 6.00 s until the fuel is exhausted. After that, the rocket is in free fall.
Find the maximum height ymax reached by the rocket. Ignore air resistance and assume a constant free-fall acceleration equal to 9.80 m/s^2 .
Answer:
Approximately [tex]7.41 \times 10^{3}\; {\rm m}[/tex].
Explanation:
If initial velocity, final velocity, and time taken are all found, then the change in height (displacement) can be found as:
[tex]\begin{aligned}(\text{displacement}) &= \frac{(\text{average velocity})}{(\text{time taken})} \\ &= \frac{(1/2)[(\text{initial velocity}) + (\text{final velocity})]}{(\text{time taken})}\end{aligned}[/tex].
For example, during the [tex]t = 6.00\; {\rm s}[/tex] of constant acceleration at [tex]a = 58.8\; {\rm m\cdot s^{-2}}[/tex], initial velocity was [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex] and final velocity would be:
[tex]\begin{aligned}v &= (\text{initial velocity}) + (\text{acceleration}) \, (\text{time}) \\ &= (0\; {\rm m\cdot s^{-1}}) + (58.8\; {\rm m\cdot s^{-2}})\, (6.00\; {\rm s}) \\ &= 352.8\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
Displacement during this period of time would be:
[tex]\begin{aligned}(\text{displacement}) &= \frac{(\text{average velocity})}{(\text{time taken})} \\ &= \frac{(1/2)[(\text{initial velocity}) + (\text{final velocity})]}{(\text{time taken})} \\ &= \frac{(1/2)\, (0\; {\rm m\cdot s^{-1}} + 352.8\; {\rm m\cdot s^{-1}})}{(6.00\; {\rm m\cdot s^{-1}})} \\ &\approx 1.058\times 10^{3}\; {\rm m}\end{aligned}[/tex].
During the next part of the flight, initial velocity was [tex]352.8\; {\rm m\cdot s^{-1}}[/tex] (from the first part of flight) and final velocity would be [tex]0\; {\rm m\cdot s^{-1}}[/tex] when the rocket reaches maximum height. Acceleration was given to be [tex]a = (-9.80\; {\rm m\cdot s^{-2}})[/tex](negative since the rocket is accelerating downward,) but time is not known. Apply the following equation to find the change in height (displacement):
[tex]\begin{aligned}(\text{displacement}) &= \frac{[(\text{final velocity})^{2} - (\text{initial velocity})^{2}]}{2\, (\text{acceleration})} \\ &\approx \frac{(0\; {\rm m\cdot s^{-1}})^{2} - (352.8\; {\rm m\cdot s^{-1}})^{2}}{2\, (-9.80\; {\rm m\cdot s^{-2}})} \\ &\approx 6.350\times 10^{3}\; {\rm m}\end{aligned}[/tex].
The total change in height would be approximately [tex](1.058\times 10^{3}\; {\rm m}) + (6.350\times 10^{3}\; {\rm m}) \approx 7.41\times 10^{3}\; {\rm m}[/tex].
A 0.22-kg ball on a stick is whirled on a vertical circle at a constant speed. when the ball is at the three o'clock position, the stick's tension is 16 n. find the tension in the stick when the ball is (a) at the twelve o'clock and (b) at the six o'clock positions.
a) The tension in the stick when the ball is at twelve o'clock is 6N.
b) And at the six o'clock position is also 16N.
To determine the tension in the stick when the ball is at the three o'clock, twelve o'clock, and six o'clock positions, we can use the equation:
T = m × v² / r
where T is the tension in the stick, m is the mass of the ball, v is the speed of the ball, and r is the radius of the circle.
In this case, the mass of the ball is 0.22 kg, the speed of the ball is constant, and the radius of the circle is the same at all positions. Therefore, the tension in the stick will be the same at all positions.
Plugging the values for the mass and radius of the circle into the equation gives us the following:
T = 0.22 kg × v² / r = 16 N
Therefore, the tension in the stick when the ball is at the three o'clock, twelve o'clock, and six o'clock positions is 16 N.
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F= 10k F2 12k F3 = 18k Problems analytical solutions using force components. check graphically 2.9 three members of a truss frame into a steel gusset plate as shown. all forces are concurrent at point o. determine the resultant of the three forces that must be carried by the gusset plate.
The resultant of the three forces that must be carried by the gusset plate is 22.14k
The resultant itself means total or amount. So, it can be said that the resultant force is the total or overall force acting on a system. The resultant force is a vector quantity.
F₁
sin 30° = x₁/10k
x₁ = 10 × sin 30° × k
x₁ = 5k
Similarly:
y₁ = 10k × cos30°
y₁ = 10k × 0.866
y₁ = 8.66k
F₂
The angle at F₂ is 0 degrees θ = 0°
So:
x₂ = -12k
y₂ = 0
F₃
cos 45° = x₃/18k
x₃ = 18 × cos 45° × k
x₃ = 12.728 k
Similarly:
y₃ = 18k × sin 45°
y₃ = 18k × 0.707
y₃ = 12.728 k
Resultant of x:
x = x₁ - x₂ + x₃
x = 5k -12 k + 12.728 k
x = 5.726 k
Resultant of y:
y = y₁ - y₂ + y₃
y = 8.66k - 0k + 12.728 k
y = 21.388k
Resultant F:
F = [tex]\sqrt{x^2 + y^2}[/tex]
F = [tex]\sqrt{ 5.726^2 + 21.388^2 }[/tex]
F = [tex]\sqrt{ 32.787+ 457.446 }[/tex]
F = [tex]\sqrt{ 490.233 }[/tex]
F = 22.14k
So, the resultant of the three forces is 22.14k
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study smarter a charged capacitor and an inductor are connected in series at time t 0. in terms of the period t of the resulting oscillations, determine how much later the following reach their maximum value: (a) the charge on the capacitor; (b) the voltage across the capacitor, with its original polarity; (c) the energy stored in the electric field; and (d) the current.
Alternate Approach The inductor exhibits open circuit behavior at time t=0+. At t=0+, inductive reactance is infinite, causing the inductor to initially operate as an open circuit. The inductor similarly acts like a short circuit at steady state.
At time t 0, what is an inductor?The inductor behaves as an open circuit with current reflected back at time t = 0 +. Important Information: A capacitor with a zero starting condition behaves as a short circuit at time t = 0 +, reflecting back voltage.
when an inductor and a charged capacitor are coupled?At time t = 0, an inductor is coupled to a charged capacitor. Considering the capacitor and the inductor as one, Write out the equation for the effective potential difference across the combination at any instant in time t, and then solve it to find the instantaneous current through the combination.
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