Use the work-energy theorem to solve each of these problems. You can use Newton\

Question

Use the work-energy theorem to solve each of these problems. You can use Newton's laws to check your answers. Neglect air resistance in all cases.

Part A

A branch falls from the top of a 87.0-m-tall redwood tree, starting from rest. How fast is it moving when it reaches the ground?

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Part B

A volcano ejects a boulder directly upward 529m into the air. How fast was the boulder moving just as it left the volcano?

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Part C

A skier moving at 5.40m/s encounters a long, rough horizontal patch of snow having coefficient of kinetic friction 0.220 with her skis. How far does she travel on this patch before stopping?

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Part D

Suppose the rough patch in part C was only 2.80m long? How fast would the skier be moving when she reached the end of the patch?

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Part E

At the base of a frictionless icy hill that rises at 25.0? above the horizontal, a toboggan has a speed of 12.0 m/stoward the hill. How high vertically above the base will it go before stopping?

Explanation / Answer

D. Suppose the rough patch in part C was only 2.80 long? How fast would the skier be moving when she reached the end of the patch?

final KE = initial KE - work by friction

(1/2) m v^2 = (1/2) m v^2 - umgd

v final^2 = v init^2 - 2ugd = 5.40^2 - 2*0.220*9.8*2.80 = 17.0864

v final = 4.133 m/s

E. At the base of a frictionless icy hill that rises at 25.0 above the horizontal, a toboggan has a speed of 12.0 toward the hill. How high vertically above the base will it go before stopping?

same as A and B: v^2 = 2gh

12^2 = 2*9.8*h
h = 7.35 meters

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