Question

A child on a sled starts from rest at the top of a hill and slides down. Does the velocity at the bottom depend on the angle of the hill if:

(a) it is icy and there is no friction?

(b) there is friction (deep snow)?


I'm thinking that the angle will always be a factor, regardless of there being friction, but I'm not sure.

Answer 1

If there is no friction at all, the <i>magnitude</i> of the velocity, or the speed, will not be dependent on the angle, it only depends on the difference in elevations.

However, since the velocity includes magnitude AND direction, the change of angle will change the direction of the final velocity.

The conclusion is: without friction, the velocity will change with the angle, but the speed will not.

If there is considerable (or any) friction, much energy will be dissipated, so the final <i>speed</i> will be reduced, hence it will change both the speed and the velocity.