Ski Jump (Conservation of Energy)

[Albeaver89]

Homework Statement

A skier (m=55.00 kg) starts sliding down from the top of a ski jump with negligible friction and takes off horizontally. (A)If h = 6.80 m and D = 10.20 m, find H.(B)Find her total kinetic energy as she reaches the ground.

Homework Equations

KEi+PEi=KEf+PEf (law of conservation of energy)
KE=1/2mv^2
PE=mgh

The Attempt at a Solution

I somehow have to find the total Height and the final Velocity. I can't seem to come up with an equation that doesn't have one of those in it...Any help would be greatly appreciated.

 

[Nessdude14]

You can find the velocity at the bottom of the ramp with the information given. You can treat it like a projectile problem, where the skier leaves the ramp at 90 degrees, with an initial height h, and lands a distance D from the ramp. Once you find this velocity, you can use the energy equations that you posted above to find H.

 

[Albeaver89]

omg...I don't see how I didn't see it before...Thank you very much!

 

[Albeaver89]

Wait...Don't you need to know how fast it's going off the ramp?

 

[Nessdude14]

Wait...Don't you need to know how fast it's going off the ramp?

First, you find the time it takes for the skier to fall height h (this is independent of the speed of the skier, since the ramp is horizontal). Then, you can find how fast the skier must have been going to travel a distance D in this time.

 

[Albeaver89]

So I got V=D/sqrt(2*h/g)
Then plug that into: m*g*H=1/2*m*(D/sqrt(2*h/g))^2 Since H=x+h we get
m*g*(x+h)=1/2*m*(D/sqrt(2*h/g))^2 then solve for x giving us:
x=((.25*d^2)/h)-h Does that seem correct?

I got -2.975?

Never mind I forgot to add in the mgh to the end of the equation silly me thanks again for all your help:)