AP Physics
posted by Elise Brown on .
A frictionless plane is 13.1 m long and inclined at 39.8 deg;. A sled starts at the bottom with an initial speed of 4.99 m/s up the incline. When the sled reaches the point at which it momentarily stops, a second sled is released from the top of the incline with an initial speed vi. Both sleds reach the bottom of the incline at the same moment. the acceleration of gravity is 9.8m/s/s. find the distance the first sled traveled up the incline.

This problem has nothing to do with the second sled or the length of the plane as long as it does not overshoot and fly off the top.
Kinetic energy at bottom = potential energy stopped at top of trajectory.
(1/2) m Vi^2 = m g h = m g (x sin theta)
x = Vi^2 / (2 g sin theta)