# Ups and Downs

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(a) A ball is launched with initial speed v from ground level up a frictionless slope. The slope makes an angle theta with the horizontal. Using conservation of energy, find the maximum vertical height hmax to which the ball will climb. Express your answer in terms of v, g, and theta. You may or may not use all of these quantities.

(b) A ball is launched with initial speed v from the ground level up a frictionless hill. The hill becomes steeper as the ball slides up; however, the ball remains in contact with the hill at all times. Using conservation of energy, find the maximum vertical height hmax to which the ball will climb. Express your answer in terms of v and g.

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##### Solution Summary

The solution sets out the problem clearly and talks through the calculations step by step to find the maximum vertical height climbed by a ball launched up a frictionless slope using the conservation of energy principles.

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(a)

The initial energy is only kinetic:

Ei=1/2 mV^2

The final energy is only potential - Max height means that the object stopped moving, thus zero kinetic ...

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