How Far Must a Skier Travel to Reach 48 m/s on a 22° Slope?

[anne921]

Homework Statement

A professional skier starts from rest and reaches a speed of 48 m/s on a ski slope angled 22.0° above the horizontal. Using the work-KE theorem and disregarding friction, find the minimum distance along the slope the skier would have to travel in order to reach this speed?

Homework Equations

W = 1/2mv_f²
W = Fd = mgd

The Attempt at a Solution

1/2 mv_f² = mgdsinθ

My solution is 310 M. Is this reasonable given the scenario? It makes sense to me but one of my students is sure it is incorrect. He says that we should be using the cos θ rather than the sin θ. The solution agrees with the key. I want to be able clearly explain the situation to him.

 

[haruspex]

I always check I'm choosing correctly between sin and cos by considering the zero angle case. If theta is zero here, what will the velocity be?