Question

A sly 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 hori- zontally at the monkey, the monkey drops from the tree in a vain attempt to escape being hit. What must the minimum muzzle ve- locity of the dart be for the dart to hit the monkey before the mon- key reaches the ground?

Answer 1

31 m/s

Step-by-step explanation:

Horizontal distance is given as 70 m and vertical distance is given as 25m hence time of flight is calculated by

`t=(d)/(v_x)=(70)/(v_x)\)` where d is the horizontal distance and V_{x} is the velocity we want

Taking the initial velocity as zero and acceleration due to gravity g=9.8 m/s^2

`h=(1)/(2)gt^2\)` and to find time

`t^(2)=2*25/9.8=2.26 seconds`

`((70)/(v_x)=2.26\)`

`\(v_x=31 m/s\)`

Therefore, minimal speed is 31 m/s