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 ranger aims directly at the monkey, not realizing that the dart will follow a parabolic path and thus will fall below the monkey. 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?

Explanation / Answer

The monkey will be hit anyway if it leaves the branch irrespective of velocity of the dart.

Vx dart= V

Vx monkey = 0

Vy dart= 0.5gt2

Vy monkey=0.5gt2

Vy of monkey wrt dart(relative velocity in y direction)=Vy dart-Vy monkey

=0

Vx of monkey wrt dart (relative velocity in x direction)= Vx dart-Vx monkey

=v

since there is no relative velocity in y direction, dart will hit monkey

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