A snow skier weighing 400 N has an initial speed of 10 m/s at the bottom of a hill which is fast enough to

A snow skier weighing 400 N has an initial speed of 10 m/s at the bottom of a hill which is fast enough to just coast to the top and stop. How high is the hill? The answer is 5 m but how do you get that answer?

Use conservation of energy - since it's a skier you can assume that there's no friction anywhere. Set h = 0 at the bottom of the hill. Since he stops at the top of the hill, you know that he must not have any kinetic energy because his velocity is zero.

E tot = E ' tot
KE = mgh
(1/2)mv^2 = mgh
(1/2)v^2 = gh
h = [(1/2)v^2]/[g]
h = [(1/2)(10 m/s)^2]/[9.81 m/s^2]
h = 5.09 m

Done!

P.S. Note that the mass term cancelled out from both sides of the equation, which means that the fact that his weight is 400 N is information you don't need. The moral of the story is to always (well, most of the time) determine an expression for the variable you need and THEN sub in the numbers.

Note that the kinetic energy of the skier is:
KE = (1/2)mv^2
= Fv^2/(2g), since m = F/g.

Then, since ∆KE = ∆PE, we have:
∆KE = ∆PE ==> mgh = Fh = Fv^2/(2g).

By solving for h:
h = v^2/(2g)
= (10 m/s)^2/[2(9.8 m/s^2)]
= 5 m, to 1 s.f.

I hope this helps!