The acceleration of the Chevrolet Spark around a level turn with a radius of curvature of 70.9 m at a speed of 22.4 m/s is 7.1 m / s / s
a = v² / R
a = Centripetal acceleration
v = Linear velocity
R = Radius
v = 22.4 m / s
R = 70.9 m
a = 22.4² / 70.9
a = 7.1 m / s / s
The acceleration of a body moving around in a circle is called as centripetal acceleration. It is a vector quantity. It can be denoted as m / s²
Therefore, the acceleration of the car is 7.1 m / s / s
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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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beginning with earth summarize the structure of the universe
Beginning with earth, the structure of the universe is Earth ← Planetary system ← Galaxy ← Universe.
An universe is made up of billons of galaxies. A galaxy is made up of thousands of planetary systems. A planet always orbit a star. In a planetary system there may be there is one planet orbiting the star or a hundreds of planets orbiting the star.
From the point of Earth, Earth is planet orbiting a star called as Sun. Hence the name of our planetary system was called a solar system. The galaxy in which our solar system is present is called as Milky way galaxy.
Therefore, beginning with earth, the structure of the universe is Earth ← Planetary system ← Galaxy ← Universe.
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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
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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Please solve with explanation
There are 14025 x10^6 grains of sand in the sand box when it is full when there was present on average 55 grains in the box initially.
How come the total grains of sand be 92,812,50 grains of sand when it is full?To solve this question we will be converting the sides to mm , 1.5 x 1000 = 1500 m.For 10 x 10 =100 , 1500x 1500x100= 25,50,00,000 mm^3, this is the volume of the box in cubic mm.Then 25,50,00,000 x55= 14025 x10^6 grains of sand in the sand box when it is full.To solve out this kind of question converting the units to mm will be better to know the precise value.To know more about mm^3 units visit:
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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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When graphic scores first evolved, what were they often used in combination with?
A. Traditional music notation
B. Numerical systems
C. Bar charts
When graphic scores first evolved, what were they often used in combination with (A) Traditional music notation .
A graphic score makes use of uses images, shapes and snap shots rather than notes. Composers use image scores because they allow them to explicit musical ideas that couldn't be described by way of traditional notation.
They advanced a new manner of visualizing song called image scores or picture notation. Photo rankings frequently appearance very specific to traditional musical rankings. In preference to strains and dots on a musical stave, photograph ratings can use all sorts of special pictures and logos to tell the performer what to play.
Graphic notation in its present day shape first appeared in the 1950s as an evolution of movement of Indeterminacy as pioneered by using John Cage.
Divide a large piece of paper into four sections and draw a motif in every. Ensure the motifs are as contrasted as possible. The score works with someone to factor on the sections. whilst they're touching a segment, a corresponding sound is played.
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How would the intensity of a sound wave change if you were to move 2 time closer to the source?
The intensity increased by a factor of 4 if the distance from the source dropped by a factor of 2.
Does distance affect intensity?Light intensity and distance are inversely correlated; as the distance grows, light intensity decreases.
What is the name for a sound wave's intensity?Sound intensity, also known as acoustic intensity, is the force carried by sound waves per unit area in a direction perpendicular to that region. The watt per square meter (W/m2) is the SI unit of intensity.
How can you gauge intensity?I = P/A, where I stands for intensity, P for power, and A for area, is the standard formula for intensity.
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The Eiffel Tower in Paris weighs 9,000 tons and stands on an area of 450 m2. Find the pressure it exerts on the ground.
Answer: The question asks us to find the pressure exerted by the Eiffel Tower on the ground. To answer this question we use the formula
pressure=Force/Area
and obtain the answer Pressure exerted by Eiffel Tower on the ground =[tex]196000 Pa[/tex]
Explanation: To find the pressure exerted by the Eiffel Tower on the ground we use the formula
[tex]pressure = \frac{force}{area}[/tex]
Given in the problem, the weight of the Eiffel Tower= 9000 tons= 9000000 kg. Ton or kilogram(kg) is a unit of mass and we have to convert it into force
[tex]force = mass * acceleration[/tex]
acceleration due to gravity [tex]g[/tex] =9.8 m/[tex]s^{2}[/tex]
mass = 9000 tons = 9000[tex]*[/tex]1000 kg[tex]= 9000000 kg[/tex] ∵[tex](1 ton = 1000 kg)[/tex]
∴ [tex]force =[/tex] [tex]9000000* 9.8[/tex] = 88200000 N [tex](1 N(newton) = 1 kg.m/s^{2})[/tex]
Given [tex]area = 450 m^{2}[/tex]
∴[tex]pressure =\frac{force}{area}= \frac{88200000}{450} =196000 N/m^{2} = 196000 pascal= 196000 Pa[/tex]
Thus the pressure exerted by the Eiffel Tower on the ground is 196000Pa
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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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Explain the concept of an inverse squared relationship?
The concept of an inverse squared relationship explains the behavior of intensity of light and distance of the light source. As the distance of the light source increases, the intensity of light decreases.
What is concept of an inverse squared relationship?The law of inverse square law says that intensity equals the inverse of the square of the distance from the source.
Mathematically, the formula for the inverse square law is given as;
I ∝ 1/r²
where;
I is the intensity of lightr is the distance from the light sourceWhat is intensity of light?The intensity of light can be defined as the measure of the amount of power emitted by a given surface or reflected by the surface.
Thus, the inverse square law is all about the inverse relation between the intensity of light or power output of a given surface to the distance of the light source.
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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.
The attached doc is my question.
Gravitational, elastic, and chemical energy are forms of potential energy.
Both kinetic and potsential energy increases with mass.
Ball on the edge of the cliff
A ball is thrown up into the air and rises until it begins to fall
Can be transformed into other form of energy.
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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A stuntman drives a car with a mass of 1800 kg on a drawbridge. The car
accelerates resulting from a constant force of 8200 N. While he is driving, the
drawbridge is raised to an incline of 30°. What is the car's new acceleration
on this incline, ignoring the force due to air resistance? (Recall that g = 9.8
m/s²)
30⁰
Force accelerating car
Weight
A. 0.3 m/s²
B. 1.2 m/s2
C. -2.5 m/s²
D. 4.0 m/s²
Halp
The acceleration of the car is now found to be 0.3 m/s². Option A
What is the acceleration?We have to recall that the acceleration is the rate at which the velocity is changed with respect to time. We know that we must take into account that the car is now moving on an inclined plane as we can see in the image attached to the question above for our scrutiny.
Now;
The force that pushes the car forward is the 8200 N force that have been stated in the question.
The component of the weight of the car that can be seen to be effective along the inclined plane is; 1800 Kg * 9.8 m/s^2 * sin 30
= 8820 N
Then we know that;
F - Wp = ma
F = constant force
Wp = effective component
m = mass
a = acceleration
Then;
a = F - Wp/m
a = 8200 N - 8820 N/1800 kg
a = 0.3 m/s²
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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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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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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)?
The scientific method is?
A) A way to use scientific measurements
B) A group of logical science questions
C) A method used to answer scientific question
D) A series of random science discoveries
These are all different questions. (Physics)
A: If a 2,000 kilograms truck is moving at 35 m/s, what is its momentum?
B: An impulse of 24 Ns acts on a baseball from a bat. What is the force applied to the ball from bat if the ball is in contact with the ball for only 0.0007s.
C: An 8 kilogram bowling ball is rolling in a straight line toward you. If its momentum is 16 kg·m/sec, how fast is it traveling?
D: A beach ball is rolling in a straight line toward you at a speed of 0.5 m/s. Its momentum is 0.25 kg·m/sec. What is the mass of the beach ball?
The momentum of truck is 70,000kg.m/s
Newtonian mechanics, the linear momentum is the product of the mass and velocity of an object. It is a vector quantity, having a magnitude and a direction. If m is an object's mass and v is its velocity, then the object's momentum p is given as,
p = mv
We are given here,
Mass of the truck = m = 2000kg
Velocity of the truck = v = 35m/s
Therefore , to get the value of momentum p using the above equation ,
p = (2000kg) × (35m/s)
p = 70000 kg. m/s
Thus , the momentum of the truck can be given as 70,000kg.m/s
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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.
An electron with a speed of 1.1 ✕ 107 m/s moves horizontally into a region where a constant vertical force of 5.1 ✕ 10−16 N acts on it. The mass of the electron is 9.11 ✕ 10−31 kg. Determine the vertical distance the electron is deflected during the time it has moved 29 mm horizontally.
Answer:
Sv = 1/2 a t^2 equation describing vertical distance traveled
Sv = 1/2 F / m * t^2 need to find t
Sh = .029m horizontal distance traveled
.029 m = Vh t time to travel 29 mm
t = 29E-3 m / 1.1E7 m/s = 2.64E-9 s
Sv = 1/2 * 5.1E-16 / 9.11E-31 * (2.64E-9)^2 = 5.1 / 2 * 2.64^2 / 9.11 * 10^-3 m
Sv = .00195 m = 1.95 mm
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.
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).
How much work is done by the force if the object moves from x = 0.15 m to x = 0.60 m ?
The work done by the force if the object moves from x = 0.15 m to x = 0.60 m is 0.24 J
What is work done by a force?The work done by a force is defined as the product of force and distance traveled.
Work done = force * distanceWork done between 0.15 m to 0.25 m = 0.6 * (0.25 - 0.15)
Work done between 0.15 m to 0.25 m = 0.6 * (0.10)
Work done between 0.15 m to 0.25 m = 0.06 J
Work done between 0.25 m to 0.50 m = 0.4 * (0.50 - 0.25)
Work done between 0.25 m to 0.50 m = 0.4 * (0.25)
Work done between 0.25 m to 0.50 m = 0.1 J
Work done between 0.50 m to 0.60 m = 0.8 * (0.60 - 0.50)
Work done between 0.50 m to 0.60 m = 0.8 * (0.10)
Work done between 0.50 m to 0.60 m = 0.08 J
Total work done = 0.06 + 0.08 + 0.1
Total work done = 0.24 J
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A toaster oven ( 1500 w), an large AC unit ( 1700 w), and 100 watt bulb are connected in parallel with a 120 volt. Determine the total energy used by these appliances in a day in kwh. The time of usage for the toaster over is 1 hour. ac 12 hours, and 100 w bulb 10 hours
In order to calculate the energy used per day by each appliance, let's multiply the power by the amount of time used in a day:
[tex]E=W\cdot t[/tex]For the toaster oven, we have:
[tex]E_1=1500\cdot1=1500\text{ Wh}=1.5\text{ kWh}[/tex]For the AC, we have:
[tex]E_2=1700\cdot12=20400\text{ Wh}=20.4\text{ kWh}[/tex]For the bulb, we have:
[tex]E_3=100\cdot10=1000\text{ Wh}=1\text{ kWh}[/tex]So the total energy used in a day is:
[tex]\begin{gathered} E=E_1+E_2+E_3 \\ E=1.5+20.4+1 \\ E=22.9\text{ kWh} \end{gathered}[/tex]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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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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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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