An injured monkey sits perched on a tree branch 3.0 m above the ground, while a

Question

An injured monkey sits perched on a tree branch 3.0 m above the ground, while a wildlife veterinarian is kneeling down in the bushes 82.0 m away attempting to subdue the monkey with a tranquilizer gun. The vet knows that the moment the gun fires the monkey will be frightened and fall down from the branch.

What angle up from the ground must the veterinarian aim the gun so that the tranquilizer dart will hit the falling monkey?

Given the angle above, what is minimum speed the tranquilizer dart must leave the gun to still hit the monkey?

Explanation / Answer

here,

Part A:

The vet aims at the monkey. Gravity acting on the dart and the monkey will result in a hit.

So the angle is

theta = arctan(Tanopposite/adjacent)

theta = arctan(3 m /82 m)  

angle = 2.1 degrees

The minimum speed is the Range to the base of the tree. The dart hits just as the monkey hits the ground

range = v0^2 sin(2 theta) /g

82 m = v0^2 * sin (2 * 2.1) / 9.8 m/s^2

solving for v0

v0 = 104.7 m/s

the minimum initial speed is 104.7 m/s

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