Use the work-energy theorem to solve each of these problems. Youcan use Newton's laws to check your answers. Neglect air resistancein all cases.
a) A branch falls from the top of a96.0-m-tall redwood tree, startingfrom rest. How fast is it moving when it reaches the ground?
b) A volcano ejects a boulder directly upward 510 m into the air. How fast was the bouldermoving just as it left the volcano?
c) A skier moving at 5.45 m/sencounters a long, rough horizontal patch of snow havingcoefficient of kinetic friction 0.220 with her skis. How far does she travel on this patch before stopping?
d) Suppose the rough patch in part (c) was only 2.90 m long? Howfast would the skier be moving when she reached the end of thepatch?
e) At the base of a frictionless icy hill that rises at 25.0°above the horizontal, a toboggan has a speed of 10.0 m/s toward the hill. How high verticallyabove the base will it go before stopping?