A skier is gliding along at 5.0 m/s on horizontal, frictionless snow. He suddenly starts down a 12° incline. His speed at the bottom is 15 m/s.
(a) What is the length of the incline in meters?
(b) How long does it take him to reach the bottom in seconds?
EM
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(a)
(initial kinetic energy) + (gravitational potential energy) = (final kinetic energy)
m(vo)^2/2 + mgh = m(vf)^2/2
(vo)^2 + 2gh = (vf)^2
h = [(vf)^2 - (vo)^2] / (2g)
h = [(15 m/s)^2 - (5.0 m/s)^2] / (2*9.81 m/s^2)
h = 10.19 m
L = 10.19 / sin12° = 49.0 m
(b)
L = (average velocity)(time)
L = [(v0 + vf)/2](t)
49.0 m = [(5.0 + 15 m/s)/2](t)
t = 4.9 s