Calculating Potential Height of Kinetic Energy Jump

[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.

 

[quasar987]

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

 

[dextercioby]

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

Daniel.

 

[Linco]

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.

 

[dextercioby]

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

Daniel.

 

[Linco]

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

 

[Doc Al]

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

 

[Linco]

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

 

[Doc Al]

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

 

[Linco]

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 height would equal 50 meters?

 

[Doc Al]

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

 

[Linco]

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?

 

[dextercioby]

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

Daniel.

 

[Linco]

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?

 

[dextercioby]

It's 100 divided by 19.2.

Daniel.