Chapter 7, Problem 13TE

A park ranger shoots 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 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? Defend your answer.

To determine

Whether the monkey will be hit by the tranquilizing dart or not.

Answer to Problem 13TE

The monkey will be hit because the horizontal position of the dart matches the position of the monkey.

Explanation of Solution

The motion of the monkey fallen from the tree is like a free-fall motion. The monkey falls in the downward direction only due to the effect of the gravitational acceleration.

The motion of the tranquilizing dart is like a projectile motion that follows the parabolic path. The tranquilizing dart moves in the downward direction due to the vertical component of the speed of the dart and at the same time, dart also moves in the horizontal direction due to the constant horizontal speed of the dart.

The variation in the vertical position of a tranquilizing dart and a falling monkey is same, but the variation in horizontal position is not same because the horizontal component of the velocity of monkey is zero but not of the dart. The monkey will hit only by directly aiming the monkey. If the monkey is aimed above or below, then the horizontal position of dart and monkey can never be same.

Conclusion:

Therefore, The monkey will be hit because the horizontal position of the dart matches the position of the monkey.