Question

A 2.9 × 103 kg car accelerates from rest at
the top of a driveway that is sloped at an
angle of 16.0 with the horizontal. An average
frictional force of 4.2×103 N impedes the car’s
motion so that the car’s speed at the bottom
of the driveway is 4.6 m/s.
The acceleration of gravity is 9.81 m/s2 .
What is the length of the driveway?

Answer 1

x = unknown length of driveway
distance it fell: h = x sin 16

potential energy lost = m g h = m g x sin 16

Ke gained = (m/2)(4.6)^2

difference = work done by friction = 4.3*10^3 * x

so
m g x sin 16 = (m/2)4.6^2 + 4.3*10^3 x