The magnitude of vector B is determined as 8.05 units.
What is the magnitude of a vector?
The magnitude of a vector is the scalar value of a vector that can be used to describe the unit value of the vector.
The magnitude of a vector can also be described as the resultant of the vector because it is usually the single value of the vector that can be used to represent the vector.
The magnitude of vector B is calculated as follows;
|B| = √(x² + y² + z²)
where;
x is the x - component of the vectory is the y - component of the vectorz is the z - component of the vector|B| = √(4.3² + 4.5² + 5.1²)
|B| = 8.05 units
Thus, we can conclude that vector B with x, y, and z components of 4.3, 4.5, and 5.1 units, respectively, has a magnitude of 8.05 units.
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module 1 question 15
A swimmer bounces straight up from a diving board and falls feet first into a pool. She starts with a velocity of 5.00 m/s, and her takeoff point is 1.90 m above the pool.
(a) How long are her feet in the air?
s
(b) What is her highest point above the board?
m
(c) What is her velocity when her feet hit the water?
m/s
( a ) T = ( [tex]u_{y}[/tex] + √ [tex]u_{y}[/tex]² + 2 g H ) / g
T = Total time taken
g = Acceleration due to gravity
H = Height above the ground
u = 5 m / s
H = 1.9 m
g = 9.8 m / s²
[tex]u_{y}[/tex] = Y-component of initial velocity
θ = 90° ( Since she bounces straight up )
sin θ = [tex]u_{y}[/tex] / u
[tex]u_{y}[/tex] = 5 * sin 90°
[tex]u_{y}[/tex] = 5 m / s
T = ( 5 + √ 5² + ( 2 * 9.8 * 1.9 ) ) / 9.8
T = ( 5 + √ 62.24 ) / 9.8
T = 12.89 / 9.8
T = 1.32 s
( b ) v² = u² + 2 a s
v = Final velocity
u = Initial velocity
s = Displacement
Consider the y-components until the swimmer reaches the highest point of her motion,
[tex]v_{y}[/tex] = 0
a = - 9.8 m / s²
[tex]u_{y}[/tex] = 5 m / s
0 = 5² + ( 2 * - 9.8 * s )
19.6 s = 25
s = 1.28 m
Maximum height reached = 1.9 + 1.28
Maximum height reached = 3.18 m
( c ) V = √ [tex]V_{x}[/tex]² + [tex]V_{y}[/tex]²
V = Final velocity
[tex]V_{x}[/tex] = X-component of final velocity
[tex]V_{y}[/tex] = Y-component of final velocity
[tex]V_{x}[/tex] = [tex]U_{x}[/tex] ( Since there is no external force acting on x-direction )
cos θ = [tex]U_{x}[/tex] / u
[tex]U_{x}[/tex] = cos 90° * 5
[tex]U_{x}[/tex] = 0
[tex]V_{y}[/tex] = [tex]U_{y}[/tex] + a t
[tex]V_{y}[/tex] = 5 + ( - 9.8 * 1.32 )
[tex]V_{y}[/tex] = 5 - 12.94
[tex]V_{y}[/tex] = - 7.94 m / s
V = √ 0 + ( - 7.94 )²
V = √ 63.04
V = 7.94 m / s
Therefore,
Her feet are in the air for 1.32 sHer highest point above the board from the ground = 3.18 mHer velocity when her feet hit the water = 7.94 m / sTo know more about Projectile launched from a height
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while test flying the new f-22 raptor fighter jet, test pilot bob put the plane in a horizontal loop while flying at the speed of sound (343 m/s). what is the minimum radius that the plane can fly if bobs centripetal acceleration cannot exceed 5g (5 times the acceleration due to gravity)?
Given
v = 343 m/s
ac = 5g
ac = 5*9.8 m/s^2
ac = 49 m/s^2
where,
v: velocity
ac = centripetal aceleration
Procedure
We call the acceleration of an object moving in uniform circular motion—resulting from a net external force—the centripetal acceleration ac; centripetal means “toward the center” or “center seeking”.
Formula
[tex]\begin{gathered} a_c=\frac{v^2}{r} \\ r=\frac{v^2}{a_c} \\ r=\frac{(343m/s)^2}{49m/s^2} \\ r=2401\text{ m} \end{gathered}[/tex]The minimum radius not to exceed the centripetal acceleration is 2401 m.
In your own words, answer the following 3 questions about an object experiencing red shift? 1. Describe the motion of an object experiencing red shift? 2. What is happening to its wavelength and frequency? 3. Why?
1. When an object is moving away from us, the light from the object is known as redshift, and when an object is moving towards us, the light from the object is known as blueshift.
2. A wavelength increases in size, and its frequency, and energy decrease.
3. The frequency of a wave increases, and its wavelength decreases.
Redshift is an important term for astronomers. The term can be taken literally. The wavelengths of light are stretched and perceived as shifting toward the red portion of the spectrum. The same thing happens to sound waves when the source moves relative to the observer.
As the wave frequency decreases, the wavelength increases as long as the wave velocity remains constant. If the wave speed stays the same as the frequency decreases, it means that fewer wave peaks or troughs pass through a given point in a given time period. The number of complete wavelengths in a given unit of time is called frequency. Frequency and energy decrease with increasing wavelength.
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draw a molecule of carbon monoxide, CO, has ____ atoms.
find the components of each vector
Answer: The direction of the resultant can be determined by finding the angle that the resultant makes with either the north-south or the east-west vector. The diagram at the right shows the angle theta (Θ) marked inside the vector addition triangle. This angle theta is the angle that the resultant makes with west.
Explanation: hope this helps.
what voltage was needed for 2 amps to flow through a 600 lamp
Answer:
See below
Explanation:
Is that 600 WATT lamp ? If so:
power = I V
600 w = 2 A * v
v = 300 v
A train of mass 55,200 kg is traveling along a straight, level track at 26.8m / s Suddenly the engineer sees a truck stalled on the tracks 184 m ahead. If the maximum possible braking force has magnitude 84.0 KN, cam the train be stopped in time? (describe overall strategy and provide all relevant details and calculations you find on related slides)
The train cannot be stopped on time after the maximum possible braking force is applied.
What is the maximum acceleration achieved by the maximum braking force?The maximum acceleration achieved by the maximum braking force is calculated as follows;
F = ma
a = F/m
where;
F is the maximum braking forcem is the mass of the traina is acceleration of the traina = (84,000) / (55,200)
a = 1.52 m/s²
The distance travelled by the train after the brake has been applied is calculated as follows;
v² = u² - 2as
where;
v is the final velocity of the train = 0 m/su is the initial velocity of the train = 26.8 m/ss is the distance travelled by the train after the brake is applied\0 = u² - 2as
2as = u²
s = u²/2a
s = (26.8²) / (2 x 1.52)
s = 236.26 m
Thus, we can conclude that the train will not be stopped on time before reaching a distance of 184 m since it will travel a total distance of 236.26 m.
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Three capacitors are connected in series. The equivalent capaci-
tance of this combination is 3.00 uF. Two of the individual capacitances
are 6.00 uF and 9.00 uF. What is the third capacitance (in uF)?
Which of the following does not correctly describe each given vector in terms of the unit vectors? (Note that each grid line is half of a unit.)
(Will give brainyist)
What are three ways that velocity can change
Answer:
Velocity is a vector quantity, meaning it is dependent on both magnitude and direction of motion. It can be changed by
1. Changing its magnitude (i.e. speed)
2. Changing the direction of motion
3. Changing both magnitude and direction.
velocity can change the three ways are, It has the ability to change direction, speed up, or slow down.
VelocityVelocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. Because the velocity vector is scalar, its absolute value magnitude will always equal the motion's speed. The SI unit of velocity is metre per second (m/s). A different way to express velocity magnitude is in centimeters per second (cm/s).velocity is the quickness or speed of motion, action, or operation. A measurement of a body's rate of motion in physics is the rate at which its location changes over time in a certain direction.To learn more about Velocity refer:
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A student wishes bulb 1 to be lit but not bulbs 2 and 3. Where must wire Y be connected?
An electric light with a wire filament that has been heated until it glows is known as an incandescent light bulb. Wire Y be connected like 4th figure. Then bulb 1 to be lit but not bulbs 2 and 3.
Who invented the electric bulb?Between 1878 and 1880, Edison evaluated more than 3,000 different bulb designs in his laboratory in Menlo Park, New Jersey, along with his research team. According to the National Archives, Edison submitted a patent application for an electric lamp with a carbon filament in November 1879.An electric light with a wire filament that has been heated until it glows is known as an incandescent light bulb.Incandescent lamp, or incandescent light globe. To prevent oxidation, the filament is encased in a glass bulb with a vacuum or inert gas.Wire Y be connected like 4th figure. Then bulb 1 to be lit but not bulbs 2 and 3.
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A car starts from rest and travels for 4.9 s with a uniform acceleration of +1.4 m/s2. The driver then applies the brakes, causing a uniform acceleration of -1.9 m/s2. The brakes are applied for 1.60 s.
(a) How fast is the car going at the end of the braking period?
(b) How far has the car gone from its start?
The car is going at speed of 3.82 m/s at the end of the breaking period and the car traveled the distance from the start is 25.33 m.
What is Acceleration?The rate of change in an object's velocity concerning time is known as acceleration in mechanics. The vector quantity of accelerations. The direction of the net force that is acting on an object determines its acceleration.
Since acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is a vector quantity as well. The definition of acceleration is the change in velocity vector over a time interval divided by the time interval.
According to the question, the given values are :
Time, t₁ = 4.9 s
Time, t₂ = 1.60 s
Acceleration, a₁ = 1.4 m/s²
Acceleration, a₂ = -1.9 m/s²
Initial Velocity, u = 0 m/s
(a)
By the Equation of motion,
v = u + a₁t₁
v = 0 + (1.4)(4.9)
v = 6.86 m/s.
Now, the velocity of the car at the end of the breaking period :
v' = v + a₂t₂
v' = 6.86 + (-1.9)(1.60)
v' = 3.82 m/s.
(b)
s₁ = ut₁ + 1/2 a₁t₁²
s₁ = 0 + 1/2 (1.4)(4.9)²
s₁ = 16.8 m.
Now for the decelerated motion :
s₂ = vt₂+1/2 a₂t₂²
s₂= 6.86(1.60) + 1/2 (-1.9)(1.60)²
s₂ = 8.53 m.
So, total distance covered from the start, D :
D = s₁ + s₂
D = 16.8 + 8.53
D = 25.33 m.
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What does the square mean in Galileo’s equation? ∆x = 1/2 a(∆t)^2
The square in Galileo’s equation means that for every given distance traveled by a falling body, the time taken is squared.
What is Galileo’s equation?Galileo’s equation is an equation that states that the distance traveled by a falling body is directly proportional to the square of the time it takes to fall.
Mathematically, Galileo’s equation is given below:
∆x = ¹/₂ a * (∆t)²
where,
∆x = the change in distancea = the acceleration due to gravity∆t² = square of the change in time.Galileo’s equation is used to calculate the distance traveled by a falling body under gravity for a given time.
It is also used to determine the time of fall from a given height.
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pressure exerted on a surface
Answer:
Pressure is defined as the force exerted on a surface divided by the area over which that force acts. Force is measured in units of Newtons (N), named after the famous scientist Isaac Newton. Area is typically measured in units of meters squared (m2).
calculate the net force acting on the box in the following. refer to the screenshot below.
Answer:
0 Newtons
Balanced
Explanation:
So for this problem, the arrows are a force, so it would be helpful to think of them as such. Since the block is being pushed to the right from the left with 4 Newtons of force, and the block is being pushed to the left and from the right with 4 Newtons of force too, the forces cancel out. Since the block isn't moving, it is balanced.
Tip: Arrows pointing to the left count as a negative force, arrows to the right count as a positive force. The net force is the total amount of force. For example, if there is a force to the left of 3 newtons, that would be represented with -3N. If a force to the right of 2 newtons is being applied to a block, the force would be 2N. Let's say that a block is being pushed to the left with 3 newtons of force and pushed to the right with 2 newtons, the net force would be -3N + 2N, which is -1N of force. -1 isn't zero, so the forces aren't balanced
1. Net force is Zero.
2. The forces are Balanced.
What is called force?The definition of force is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.The newton serves as the SI unit of force.Two main categories can be used to classify forces: Force yourself to. Forces without contact.Without force, individuals would not be able to open and close objects, lift our arms and legs, or do anything else for that matter. This has an impact on how we conduct our daily lives.To learn more about : force
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you jump off a cliff and accelerate at 9.8 m/s^2 due to gravity. How fast are you falling after 12.0 seconds?
By the speed of 117.6 m/s you falling after 12.0 seconds.
Free fall formula,
v = -gt
v = velocity of free fall
g = acceleration due to gravity, Given = 9.8 m/[tex]s^{2}[/tex]
t = time, Given = 12s
Put these values in formula, v = -gt
v = - 12 × 9.8
v = 117.6 m/s.
Hence, by the speed of 117.6 m/s you falling after 12.0 seconds.
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A train accelerates from 36 km/h to 54 km/h in 10 seconds. Find the acceleration and distance traveled by the train.
SORRY IF IN WRONG SECTION. ANSWER FOR 50 POINTS. 1. The chemical process by which your body breaks down the nutrients in foods to release energy (1 point) for the cells in your body describes OCalories Ocholesterol Ometabolism Onutrition
Metabolism is the chemical process by which your body breaks down the nutrients in foods to release energy for the cells in your body (Option 3).
What is Metabolism?The term Metabolism makes reference to all chemical reactions by which the body can obtain energy from foods by breaking them down into smaller elements. The breakdown of chemical bonds releases energy, which is used to generate Adenosine triphosphate, the energy coin of the cells.
Metabolism has two major categories:Catabolism or metabolic pathways where foods are reduced to smaller molecules that are used for oxidation and thus the production of energy.Anabolism or metabolic pathways aimed at generating complex molecules from simpler ones.Therefore, we can conclude that metabolism refers to the groups of pathways by which an organism breaks down nutrients such as proteins or carbohydrates in order to obtain energy for cells and perform diverse activities (e.g. growth, differentiation, etc)
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Certain iguanas have been observed to run as fast as 10.0m/s.Suppose an iguana runs in a straight line at this speed for 5.00 s. The direction of motion makes an angle of 30.0° to the east of north. Find the value of the iguana’s northward displacement.
The value of the iguana’s northward displacement is 1 meter.
The velocity V of iguana is 10m/s.
The time for which iguana runs is 5 seconds.
The angle it is making with the north is 30°.
The velocity of iguana will have two components now,
One along east and one along north.
The component along east is Vcos(30°).
And the component along north is Vsin(30°).
The horizontal displacement of the iguana is,
Northward displacement = northward velocity × time.
The northward velocity is 10sin(30°).
Time is 5 seconds no matter where the iguana moves.
So,
Northwards displacement = 10sin(30°)/5
Northwards displacement = 10/10 = 1m
The displacement in north is 1 meter.
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Not sure how to do part a, b and c
Variables typically consist of space, time, and occasionally parts of momentum. The bicycle eventually travels at 13.8 m/s.
what exactly does momentum mean?According to Newtonian mechanics, an object's mass and velocity are combined to form its linear momentum, translational momentum, or just momentum. As a vector quantity with both a magnitude and a direction, it has both. When an object's mass (m) and velocity (v), another vector quantity, are known, the object's momentum (p) is also known.
what is significance of momentum?An object's mass, velocity, and direction are related by the concept of momentum. Force is produced whenever momentum changes. As a result, the force pushing against the object is identified by a change in momentum.
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1. At the bottom of the screen, switch to the Measure section.
2. On either the 3rd or the 4th track, bring your skater to the top left, and let your
skater go. Keep Stick to Track turned on so that your skater cannot fall off the track or jump
off the surface. Set friction to none.
3. Release your skater from the top left side of the track, and then pause when your skater
reaches the top right side of the track. There will be a trail of dots visible on the track. You
can click and drag the target of the data measuring tool onto different dots. It will then
display the values of the different forms of energy as well as the speed and height of the
skater when they were at the position of the dot your target is over.
4. Choose 10 data points that are distributed around the track. Try to pick data points on the
left, bottom, middle, right, top. In other words, a "random" sampling. Record the statistics
of these data points in the chart below. Double click on the cells to enter values
Height (m)
Speed (m/s)
Potential Energy (J) Kinetic Energy (J)
Data Point
1
2
3
4
5
6
7
8
Kinetic energy has the following formula:
K.E. = 1/2 m v2, where m is the object's mass and v is its square velocity. The standard unit of kinetic energy measurement is the Joule (J), which is equal to 1 kg/m2/s2.
Potential energy: Potential energy is the power that a thing possesses as a result of where it is in relation to other objects. The formula for gravitational force is P.E. = mgh, where g is the acceleration caused by gravity (9.8 m/s2 at the earth's surface) and h is the height in meters.Height: In a three-dimensional, visual world, height is a physical characteristic that naturally gains enormous importance.Data point: A discrete unit of information is called a data point. Any single fact is a data point, broadly speaking. The singular form of data, or datum, is roughly equal to the term "data point."
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What mathematical relationship between variables is suggested by a graph showing an L-shaped hyperbola that drops and flattens quickly?
Inverse (simple)
Inverse-squared
Linear (direct)
Quadratic (power)
The mathematical relationship between variables is suggested by a graph showing an L-shaped hyperbola that drops and flattens quickly is option A: Inverse (simple).
What is a inverse relationship in math?When two variables change in an inverse relationship, they do so in the opposite directions: one increases while the other drops, and vice versa. Y declines as X rises in an inverse relationship. An inverse relationship always has a negative slope on a graph.
A function that can be altered into another function is said to be one that can be seen as an inverse function or what we call the anti-function.
Therefore, Inverse operations are a class of mathematical operations where one operation cancels out the effects of another and it best shows L-shaped hyperbola.
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Answer:
B. Inverse-squared
Explanation:
I took the physics exam
6. An astronaut and equipment weigh 2,156 N on Earth. Weightless in space, the astronaut throws away
a 5.0 kg wrench with a velocity of 5.0 m/s. What is the resulting velocity of the astronaut in the opposite
direction?
Answer:
One of the first things we need to know is the mass of the astronaut and equipment combined. Weight is given by the formula:
W = m x g, where m is the mass of the object(kg) and g is the gravitational acceleration on Earth's surface(9.8 m/s^2)
Knowing the weight of the astronaut and equipment, we get:
m = W / g
m = 2,156 N / 9.8 m/s^2 ( ^2 represents the power of 2)
m = 219.9 kg
Now, one last thing we need to know is the resulting velocity of the astronaut in the opposite direction. Once the astronaut throws the wrench from their equipment, according to the 3rd law of motion, the astronaut and the wrench will move in opposite directions because the astronaut pushed the wrench, and in return, the astronaut is pushed by the wrench. Having all these, we need to work with momentum.
p = m * v, where p is the object's momentum, m is mass and v is its velocity
let's call [tex]m_{a}[/tex] the astronaut's mass(combined with their equipment, including the wrench since it's initially part of the equipment)
[tex]m_{w}[/tex] = 5.0 kg is the wrench's mass
[tex]v_{wrench}{[/tex] = 5.0 m/s is the wrench velocity after it was thrown
The astronaut's momentum(before the thrown wrench): [tex]p_{before}=m_{a} * 0 = 0[/tex], because the astronaut's initial velocity is zero(including the equipment and wrench)
The astronaut threw the wrench. Therefore, we get the following momentum: [tex]p_{after} = m_{w} * v_{wrench} + (m_{a} - m_{w} ) * v_{after}[/tex]
The reason why we subtract the astronaut and equipment mass from the wrench's mass is that the astronaut and the equipment move independently from the wrench, therefore we exclude the wrench's mass.
The 3rd law of motion also implies that the total momentum of a system of objects interacting(colliding against one another) doesn't change. Therefore:
[tex]p_{before} = p_{after}[/tex]
Plugging all the values, we get:
5.0 kg * 5.0 m/s + (219.9 kg - 5.0 kg) * [tex]v_{after}[/tex] = 0
Solving the above equation, we get that the resulting velocity of the astronaut in the opposite direction is:
[tex]v_{after}=-8.596 m/s[/tex]
Note: The minus denotes the opposite direction the astronaut has after it was pushed by the wrench.
(1) If a man lifts a a 20-kg
bucket from a well and does 6
kJ of work, how deep is the
well? Assume the speed o the
bucket remains constant as it is
lifted.
If a man lifts a a 20-kg bucket from a well and does 6 kJ of work, the well will be 30.6 m deep.
W = m g h
W = Work
m = Mass
g = Acceleration due to gravity
h = Height
m = 20 kg
g = 9.8 m / s²
W = 6 KJ
W = 6000 J
h = W / m g
h = 6000 / 20 * 9.8
h = 30.6 m
W = m g h is derived from W = F * d. According to Newton's second law of motion, F = m a. Since the object is moving vertically upwards, a = g. Therefore, F = m g and hence W = m g h
Therefore, the well is 30.6 m deep
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Is water in the air a source of radiation or convection?
How is air in a hot air Ballon convection?
Answer: Convection
Explanation: in its simplest form is the transfer of heat through circulating air and liquids, this works inside of a hot air balloon by heating the inside of the air with a burner located at the bottom of the balloon, this then makes the air inside of the balloon less dense or lighter than the cooler air on the outside, causing the balloon to float upwards.
Disturbed by speeding cars outside his workplace, Nobel laureate Arthur Holly Compton designed a speed bump (called the "Holly hump") and had it installed. Suppose a 1800-kg car passes over a hump in a roadway that follows the arc of a circle of radius 21.4 m as in the figure below.(a) If the car travels at 26.6 km/h what force does the road exert on the car as the car passes the highest point of the hump?(b) What is the maximum speed the car can have without losing contact with the road as it passes this highest point?
ANSWER
[tex]\begin{gathered} (a)13,046N \\ (b)14.5m\/s\text{ or }52.2km\/h \end{gathered}[/tex]EXPLANATION
Parameters given:
Mass of the car, m = 1800 kg
Radius of arc, r = 21.4 m
(a) First, let us make a free body sketch of the problem:
where N = force exerted by the road on the car
W = weight of the car
v = velocity of the car
First, let us convert the given velocity to meters per second:
[tex]\begin{gathered} v=26.6\cdot\frac{1000}{3600} \\ v=7.39m\/s \end{gathered}[/tex]The centripetal force acting on the car as it moves in the semi-circular arc is given by:
[tex]F=\frac{mv^2}{r}[/tex]The total forces acting on the car is:
[tex]N-W+F=0[/tex]This implies that:
[tex]\begin{gathered} N=W-F \\ N=mg-\frac{mv^2}{r} \\ N=(1800\cdot9.8)-\frac{1800\cdot7.39^2}{21.4}=17,640-4,593.54 \\ N=13,046N \end{gathered}[/tex]That is the force that the road exerts on the car.
(b) At the maximum speed, the car will start to lose contact with the road at N = 0:
[tex]\begin{gathered} \Rightarrow0=W-F \\ 0=mg-\frac{mv^2_m}{r} \\ \Rightarrow\frac{mv^2_m}{r}=mg \\ \Rightarrow v^2_m=gr \\ \Rightarrow v_m=\sqrt[]{gr} \end{gathered}[/tex]Substitute the values of g and r to solve for maximum speed, vm:
[tex]\begin{gathered} v_m=\sqrt[]{9.80\cdot21.4} \\ v_m=\sqrt[]{209.72} \\ v_m=14.5m\/s \end{gathered}[/tex]In km/h, that is:
[tex]\begin{gathered} 14.5\cdot\frac{3600}{1000} \\ 52.2km\/h \end{gathered}[/tex]That is the maximum speed that the car can have.
A runner is jogging in a straight line at a
steady v,= 2.5 km/hr. When the runner is
L= 4.4 km from the finish line, a bird begins
flying straight from the runner to the finish
line at = 10 km/hr (4 times as fast as the
runner). When the bird reaches the finish
line, it turns around and flies directly back to
the runner.
The cumulative distance travelled by the bird is 11.5 Km.
The speed of the jogger is 6.1 km/h.
Speed of the bird is 30.5 km/h.
The distance between the finish line and the jogger is 6.9 Km.
Now, as we know that the bird starts with the jogger and reaches the finish line early and then returns back to the jogger. Assuming no loss in velocity while change the velocity.
We can understand that the time period of travel of the jogger and the the bird is t.
As we know,
Let us say that the distance that the jogger coves in time t is x.
So the distance travelled by the bird is,
Distance travelled till finish line plus the distance between jogger and finish line.
Distance travelled by bird = 6.9+6.9-x
Now as we know,
Time = distance/speed.
For jogger,
t = x/6.1
For the bird,
t=6.9+6.9-x/30.5
We can write,
x/6.1 = 13.8-x/30.5
30.5x =13.8(6.1)-6.1x
x(30.5+6.1) = 84.18
x = 2.3 Km.
The total distance travelled by the bird is 13.8-x
The total distance travelled by bird = 11.5Km.
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A runner is jogging in a straight line at a steady v = 6.1 km/hr. When the runner is L = 6.9 km from the finish line, a bird begins flying straight from the runner to the finish line at v = 30.5 km/hr (5 times as fast as the runner). When the bird reaches the finish line, it turns around and flies directly back to the runner.
a. What cumulative distance does the bird travel? Even though the bird is a dodo, assume that it occupies only one point in space (a "zero" length bird), travels in a straight line, and that it can turn without loss of speed. Answer in units of km.
1 (a) A large stone, initially at rest, falls from the top of a building. The stone takes 3.2s to fall to the ground. For this stone, air resistance can be ignored.
(i) Stating the formula that you use, show that the speed of the stone when it hits the ground is 32 m/s.
The formula that can be used to show that the speed of the stone when it hits the ground is 32 m/s is v = u + at
According to equations of motion,
v = u + at
v = Final velocity
u = Initial velocity
t = Time
a = Acceleration due to gravity
t = 3.2 s
a = 10 m / s²
v = 0 + ( 10 * 3.2 )
v = 32 m /s
Equations of motion are used to describe the position of a moving object in a constantly accelerated manner. The position can be described using acceleration, velocity, displacement and time.
Therefore, the formula that can be used to show that the speed of the stone when it hits the ground is 32 m/s is v = u + at
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A heat engine converts 100.0 cal from a supply of 400.0 cal into work. How much mechanical work was done?
A heat engine converts 100.0 cal from a supply of 400 cal into work. Hence, the mechanical work done will be 25%.
What is Heat Engine?A heat engine normally expels heat that can't be used to perform work after using energy supplied in the form of heat to do so. The study of the interactions between heat and work is known as thermodynamics. The operation of a heat engine is restricted by the first and second laws of thermodynamics.
The first law applies the principle of energy conservation to the system, and the second law establishes upper and lower bounds on the machine's potential efficiency and specifies the direction of energy flow.
According to the question,
Mechanical work done = 100/400
= 0.25 or,
Work done = 25%.
Hence, the mechanical work done will be 25 %.
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An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope stretched between the cliffs. He stops to rest at the middle of the rope. The rope will break if the tension in it exceeds 2.55×10^4 N, and our hero's mass is 85.6 kg.
A) If the angle between the rope and the horizontal is θ = 10.5∘, find the tension in the rope.
B) What is the smallest value the angle θ can have if the rope is not to break?
The tension in the rope and the smallest value the angle θ can have if the rope is not to break
[tex]\theta=0.966 \textdegree[/tex]T=2232 NThis is further explained below.
The smallest value the angle θ can have if the rope is not to break:Generally, the equation for the tension is mathematically given as
[tex]2 T sin \theta = m g[/tex]
Therefore
2*T*sin(11.1) = 87.6 * 9.81
T=2232 N
the tension in the rope is T=2232 N
b)
Generally, the equation for the angle is mathematically given as
[tex]2*2.55E4*sin \theta = 87.6*9.81[/tex]
Therefore
[tex]\theta = arcsin( \frac{87.6*9.81}{(2*2.55E4))}[/tex]
[tex]\theta=0.966 \textdegree[/tex]
In conclusion, The smallest value the angle θ can have if the rope is not to break is
[tex]\theta=0.966 \textdegree[/tex]
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