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Question

A roller coaster car starts out at rest at the top of the first hill and reaches a speed of 10 m/s at the bottom of the hill. What is its speed when it is half-way down? Assume that the track is frictionless.

 

Im pretty sure it is just 5.0 m/s but im not sure.

 

Answer 1

This is another example of energy conservation.  Set kinetic energy at bottom equal to potential energy at top, solve for height h, then solve for speed using the same total energy at h/2.

 

Top:

 

mgh = (1/2)mv²

 

gh = v²/2

 

h = v²/(2g) = 10²/[2(9.8)] m = 5.1 m

 

Half way down:

 

u = speed

 

g(h/2) = u²/2

 

u = √[2g(h/2)] = √(gh) = √[(9.8)(5)] m/s = 7.0 m/s