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

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft