Conservation of Energy ski-jump ramp

[lauriecherie]

Homework Statement

A 79 kg skier leaves the end of a ski-jump ramp with a velocity of 26 m/s directed 25° above the horizontal. Suppose that as a result of air drag the skier returns to the ground with a speed of 24 m/s, landing 18 m vertically below the end of the ramp. From the launch to the return to the ground, by how much is the mechanical energy of the skier-Earth system reduced because of air drag?

Homework Equations

Total Mechanical Energy initial = Total Mechanical Energy final where Total mechanical energry is all energies added.

The Attempt at a Solution

I took gravitational potential energy initial to be mgh and added that with kinetic energy initial, which is .5*m*velocity initial ^2. I set all this equal to the same thing, but as the finals of each of these energies. Then I saw that the difference between the two is 403.16. This seems like an awful lot. The answer should be in joules. Is my answer correct?

 

[LowlyPion]

It will be more Joules than that right?

How many Joules in gravitational potential alone? And it ends with less velocity?

 

[lauriecherie]

It will be more Joules than that right?

How many Joules in gravitational potential alone? And it ends with less velocity?

I got 691.16 J for the total mechanical energy initial. For the total mechanical energy final I came out with 288 J. So it was reduced by 288 J?

 

[LowlyPion]

I got 691.16 J for the total mechanical energy initial. For the total mechanical energy final I came out with 288 J. So it was reduced by 288 J?

1/2*mv² initial = 691 J ?

Can you show your calculation?

Isn't it 1/2 * 79 * 26² ?

 

[lauriecherie]

1/2*mv² initial = 691 J ?

Can you show your calculation?

Isn't it 1/2 * 79 * 26² ?

I added the Kinetic energy plus the gravitational potential energy initial. I then set that equal to total mechanical energy final which only included kinetic energy. since I had mass on both sides I canceled out the mass. I was then left with gh + (.5*26^2) = (.5*24^2).

 

[LowlyPion]

I added the Kinetic energy plus the gravitational potential energy initial. I then set that equal to total mechanical energy final which only included kinetic energy. since I had mass on both sides I canceled out the mass. I was then left with gh + (.5*26^2) = (.5*24^2).

Ahhh. That explains it then.

You can't cancel out the mass.

You haven't accounted for the unknown work due to air resistance in your equation. You can't divide the mass out of that.