A park ranger wants to shoot a monkey hanging from a branch of a tree with a tra

Question

A park ranger wants to shoot a monkey hanging from a branch of a tree with a tranquilizing dart. The horizontal distance between the ringer and monkey is L and the height go the monkey is h. The ranger aims directly at the monkey with the angle theta from the ground. The monkey, however, sees the dart leave the gun and lets go of the branch to avoid being hit. Will the monkey be hit anyway? Does the velocity of the dart affect your answer, assuming that it is great enough to travel the horizontal distance to the tree before hitting the ground. Verify your answer with formula.

Explanation / Answer

As we discussed and demonstrated in class, think of the motion of both dart and monkey if we could somehow turn gravity "off" and fire the dart. Then the dart would move along a straight line and hit the monkey who would remain in place beside the tree branch. Now turn gravity back "on" and fire the dart. Now both dart and monkey fall from their "gravity-off positions" by 1/2 g t2 so the monkey will, again, be hit by the dart.

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