A 75.0 kg skier slides down a 75.0 m high slope without friction.The velocity of the skier at the bottom of the slope is
A) 20.6 m/s.
B) 29.7 m/s.
C) 38.3 m/s.
D) 40.5 m/s.
E) 50.0 m/s.

Question

Quizplus · Accepted Answer

The potential energy of the skier at the top of the slope turns into kinetic energy at the bottom of the slope, since there is no friction to dissipate the energy. Therefore, we can use conservation of energy:

PE (at top) = KE (at bottom)

mgh = 1/2mv^2

where m is the mass of the skier, h is the height of the slope, and v is the velocity of the skier at the bottom.

Plugging in the given values:

(75.0 kg)(9.81 m/s^2)(75.0 m) = 1/2(75.0 kg)v^2

Solving for v gives:

v = √(2gh)

v = √(2(9.81 m/s^2)(75.0 m))

v ≈ 38.3 m/s

Therefore, the best choice is C, 38.3 m/s.

A 750 Kg Skier Slides Down a 75