Answer to Question #181883 in Physics for adam

Question

A rescue plane is flying horizontally at a height of 97 m above ground. The pilot spots a survivor and releases an emergency kit with a parachute. The kit descends at a constant vertical acceleration of -6.63 m/s2 and the initial plane horizontal speed is 66.4 m/s. Assuming air resistance and wind are negligible, how far away from the survivor will the emergency kit hit the ground?

Answer 1

Find the time it will take to reach the ground at -6.63 m/s/s:

$$t=\sqrt{\frac{2h}{a}}.$$

Find the distance the horizontal kit will cover during this time:

$$r=vt=v\sqrt{\frac{2h}{a}}=359\text{ m}.$$