Asly 1.5-kg monkey and a jungle veterinarian with a blow-gun loaded with a tranquilizer dart are 25 m above the ground in trees 70 m apart. just as the veterinarian shoots horizontally at the monkey, the monkey drops from the tree in a vain attempt to escape being hit. what must the minimum muzzle velocity of the dart be for the dart to hit the monkey before the mon- key reaches the ground?

minimum muzzle velocity of the dart:

Explanation:

Al t time t=0, the monkey drops and the dart is shot,

For the monkey the general position equation will be:

it starts from rest so  , and the acceleration is , so

(1)

it will hit the ground when y = 0:

For the dart first we need to know the time when it reaches the monkey on the horizontal position, for this we have the equation:

In this case, neglecting the air friction acceleration will be 0, and considering the origin on the gun :

(2)

So the time when it hits the monkey would be when x = 70m:

(3)

To hit the monkey before it reaches the ground it must be

no. dot product   =0 when vecs at right angles

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