What would be the speed of a cart at the bottom of a very long frictionless incl

Question

What would be the speed of a cart at the bottom of a very long frictionless inclined plane if it was released from rest at a height of 10.0 m above the bottom of the track? Assume the bottom of the track has height = 0. Show your work. A cart is released front a height of 5 m on the left side of a U-shaped track with identical inclines on the left and right. If the cart is released from rest, how far up (height) the right side of the track will the cart travel? Assume that friction is negligible. Justify your answer. The car shown in the picture below (mass = 998 kg) has just run out of gas while moving at a speed of 15 m/s. Assuming that friction is negligible, will the car make it to the gas station if it coasts the whole way? Justify your answer.

Explanation / Answer

3)

here,

the initial height of the cart , h = 10 m

let the speed of cart at the bottom of the incline be v

using conservation of energy

potential energy lost = kinetic energy gained

m *g * h = 0.5 * m * v^2

9.8 * 10 = 0.5 * v^2

v = 14 m/s

the speed at the bottom of track is 14 m/s

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