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.

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