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Question

A 500 kg roller coaster car crests a 20 m high hill at a speed of 10 m/s. It then rolls down the other side, all the way to ground level, and climbs a second hill. What is the speed of the car when it is 10 m up the second hill?

Answer 1

Work this by setting the energies at the 2 points equal to each other, and solve for the speed.  The answer will not depend on the mass.

 

 

(1/2)mv₁² + mgh₁ = (1/2)mv₂² + mgh₂

 

(1/2)v₁² + gh₁ = (1/2)v₂² + gh₂

 

v₂ = √[v₁² + 2g(h₁ - h₂)] = √[(10)² + 2(9.8)(20 - 10)] ≅ 17.2 m/s