# Calculating Potential Height of Kinetic Energy Jump

• Linco
In summary, if a sprinter running at a speed of 10 meters per second could convert his/her kinetic energy into upward motion, how high could he/she jump? if a sprinter had a potential energy of 100 joules and converted it all to kinetic energy, his potential energy would be 50 joules and he would be able to jump 1 meter high.
Linco
If a sprinter running at a speed of 10 meters per second could convert his/her kinetic energy into upward motion, how high could he/she jump?

I understand that KE= 1/2 mass X (Speed)2 But I am really not sure how I could do this without a mass.

At the point where all is kinetic energy has been converted in potential energy.. how high will he be?

U don't need the mass of the sprinter in this elementary setup.

Daniel.

Well this elementary setup doesn't seem so elementary to me. The point where his potential energy turns into kinetic energy will be the first instance he is in motion.

It's the other way around.He's high-jumping.Which means that his KE converts into PE and not viceversa.

Daniel.

I feel stupid now. so if he used the same amount of energy he would be able to jump 10 meters high?

No. Figure it out. Set the initial KE equal to the final gravitational PE. Then you can solve for the maximum height.

This is where I am lost the only formulas that the book provides is PE=mgh and KE= 1/2mv*

So i don't see how i can solve this PE=mgh=1/2m(100)=KE

That's the correct equation: $mgh = 1/2 m v^2$; now just solve for h. (Divide both sides by mg!)

I think if I would of realized that mass and weight are directly proportional sooner I would of had less trouble with this. So the hight would equal 50 meters?

$h = v^2/(2g)$. Plug in the numbers: v = 10 m/s; g = 9.8 m/s^2.

Ok so one meter. Now the question is how did you get this formula and where did you get g=9.8 from. Wouldn't mgh=1/2mv* come out to h=1/2v*? I understand that 9.8 is that rate that things fall but I am not sure how this plugs into all this. Isn't mg that weight of the object?

U mean ~5 m...No,it wouldn't come out to what u've written.You can simplify only through "m"...

Daniel.

I didn't see the 2g in there so it's .5 meters. So when simplying you would dived 1/2m by mg to get 2g right?

It's 100 divided by 19.2.

Daniel.

## 1. What is the formula for calculating the potential height of a kinetic energy jump?

The formula for calculating the potential height of a kinetic energy jump is: Potential Height = (Kinetic Energy^2)/(2 x acceleration due to gravity). This formula is derived from the conservation of energy principle, which states that the total energy of a system remains constant.

## 2. How is kinetic energy related to potential height in a jump?

Kinetic energy and potential height are directly related in a jump. As the kinetic energy of an object increases, its potential height also increases. This is because as an object gains kinetic energy, it has more energy available to overcome the force of gravity and gain height.

## 3. What is the role of acceleration due to gravity in calculating potential height?

Acceleration due to gravity, denoted as 'g', is a constant value that represents the rate at which objects accelerate towards the Earth's surface. In the formula for potential height, acceleration due to gravity is in the denominator, which means that a higher value of 'g' will result in a lower potential height.

## 4. Can potential height be negative in a kinetic energy jump?

No, potential height cannot be negative in a kinetic energy jump. This is because potential height is a measure of the height an object can reach, and it cannot be below ground level. If the calculated potential height is negative, it means that the object does not have enough energy to overcome the force of gravity and will not be able to jump to the specified height.

## 5. What factors can affect the accuracy of calculated potential height in a jump?

There are a few factors that can affect the accuracy of calculated potential height in a jump. These include the accuracy of the initial kinetic energy measurement, the precision of the acceleration due to gravity value used, and any external forces acting on the object during the jump such as air resistance or friction with the ground.

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