Question

A child on a sled starts from rest at the top of a 15° slope. if the trip to the bottom takes 23.9 s how long is the slope? assume that frictional forces may be neglected.

Answer 1

The first thing you should do for this case is a free body diagram to find the force acting on the body in the direction of the slope.
We have then:
F = m * g * sin (15)
Also, by definition:
F = m * a
Matching:
a = g * sin (15) = 9.80 * sin (15) = 2.536 m / s ^ 2
Then, the kinematic equation for the final position in direction x is:
x = vx0 * t + 1/2 * a * t ^ 2
vx0 = 0 (Initial rest)
x = 1/2 * 2.536 * (23.9) ^ 2 = 724.3m
Answer
the slope is 724.3m long