Question

A skier with an initial speed of 12.0 m/s coasts up a 3.50-m-high rise as shown in the figure above. Find her final speed at the top, given that the friction between her skis and the snow is negligible.

Answer 1

You can figure this out using conservation of energy. Because there is no friction, all the kinetic energy the skier started with is equal to the kinetic energy the skier ends with PLUS the gravitational potential energy the skier gained by going up the hill.

\[KE_i=KE_f+PE_f\]\[\frac{1}{2}mv_i^2=\frac{1}{2}mv_f^2+mgh\]
You'll notice that the mass divides out, so it's no problem that we aren't given it in the question. You'll also notice that the angle of the hill isn't a factor at all (it would be if friction was important). So now we have:

\[\frac{1}{2}v_i^2=\frac{1}{2}v_f^2+gh\]
Plug in the values you know and solve for the final speed!

Answer 2

thank you!