A monkey in a zoo needs medical treatment by a doctor. While the monkey plays in

Question

A monkey in a zoo needs medical treatment by a doctor. While the monkey plays in a tree, the doctor fires a tranquilizer dart at the monkey who hangs from a branch a distance h vertically above the dart gun and a distance R horizontally away from the dart gun. The doctor aims directly at the monkey and fires, but just as the dart gun fires, the startled monkey drops from the branch. Show that the dart hits the monkey. Begin by drawing a diagram and choosing a coordinate system. Please write a brief strategy before setting up kinematic equations. Also, find the minimum value for the speed of the dart leaving the gun so that the monkey is hit.

Explanation / Answer

In vertical,

bullet was fired horizontally so initial vertical velcoity was zero and moneky drops it self from rest.

so initial velocity of monkey was also zero.

both have same acc. = g (acc due to gravity).

so using y = ut +at^2 /2

u = same,a = same for both bullet and monkey.

so in time, bullet and monkey both will travel same y distance.

so bullet will hit the moneky.

but bullet have to reach the monkey before it fall on the ground or in other words before it travels h distance in vertical.

using h = 0*t + g*t^2 /2

t = sqrt(2h/g)

so bullet have less sqrt(2h/g) time to travel distance R in horizontal.

so initial speed (all inhorizontal) = R / sqrt(2h/g)

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