Question

1. A rescue plane flying horizontally at an altitude of 500 m and velocity of 300 m\s east drops a food supply packet to plane crash survivors on the ground. The packet falls freely to the ground without a parachute. Assume that the weather is perfect.
a. Calculate the time it takes for the supply packet to hit the ground
b. Calculate horizontal distance

Answer 1

First note that the plane and the packet have the same horizontal velocity throughout this problem. Therefore the bomb lands exactly under the plane. If the package were a bomb, it would be wise to turn after yelling "bombs away".
anyway:
The falling problem:
falls 500 meters with zero initial vertical velocity component.
500 = (1/2) g t^2
1000 = 9.81 t^2
t = 10.1 seconds to fall 500 meters

Then the package flew for 10.2 seconds at a horizontal speed of 300 east so
d = u t = 300*10.1 = 3029 meters east