An injured monkey sits perched on a tree branch 4.5 m above the ground, while a

Question

An injured monkey sits perched on a tree branch 4.5 m above the ground, while a wildlife veterinarian is kneeling down in the bushes 88.5 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? Given the angle above, what is minimum speed the tranquilizer dart must leave the gun to still hit the monkey?

Explanation / Answer

Here ,

as there is same acceleration due to gravity acting on the monkey and tranqulizer , he should directly aim the gun at the monkey for hitting him.

hence , angle of gun from ground = arctan(height/distance)

angle of gun from ground = arctan(4.5/88.5)

angle of gun from ground = 2.91 degree

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for the minimum speed ,

time taken for monkey to fall ,t = sqrt(2 * h/g)

t = sqrt(2 * 4.5/9.8)

t = 0.958 s

minimum speed required = distance/time

minimum speed required = 88.5/0.958 m/s

minimum speed required = 92.34 m/s

the minimum speed required by the tranquilizer gun is 92.34 m/s

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