How Much Energy Is Lost Due to Air Drag in Ski Jumping?

[ViewtifulBeau]

A 49kg skier leaves the end of a ski-jump ramp with a velocity of 28 m/s directed 22o above the horizantal. Suppose that as a result of air drag the skier returns to the ground with a speed of 17 m/s, landing 10 meters vertically below 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?

first i found the velocity the skier should have without air drag (31.3075 m/s). then i found the difference between 31.3075 and the actual speed 17m/s. then i used that number and plugged it into 1/2 m v^2 = KE to find the energy lost due to air resistance. 5015 J... this isn't right though. what did i do wrong?

 

[vanesch]

first i found the velocity the skier should have without air drag (31.3075 m/s). then i found the difference between 31.3075 and the actual speed 17m/s. then i used that number and plugged it into 1/2 m v^2 = KE to find the energy lost due to air resistance. 5015 J... this isn't right though. what did i do wrong?

You shouldn't calculate the difference in velocity and then the corresponding hypothetical KE, you should take the difference between the 2 KE (with and without drag).

cheers,
Patrick.

 

[russ_watters]

Why: because KE is a square function of velocity, and therefore finding the difference in velocity and plugging that into the KE equation will give the wrong answer.