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 87.5 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?

Answer 1

here in the given situation if monkey starts free fall at the same instant when veterinarian shoots towards it then we know that vertical component of motion of monkey and the dart will be same as under gravity

so here the dart will always hit the monkey because they both moves under same acceleration

so here for the angle we can use

$tan\theta = \frac{H}{L}$

now we have

H = 3 m

L = 87.5 m

now we will have

$tan\theta = \frac{3}{87.5}$

$tan\theta = 0.034$

$\theta = 1.96 degree$

so angle will be 1.96 degree above the ground