Question

An American Red Cross plane needs to drop emergency supplies to victims of a hurricane in a remote part of the world. The plane is traveling horizontally at 100.0 m/s at a height of 50.0 m above the ground. What horizontal distance does the package travel before striking the ground?

Answer 1

Refer to the diagram shown below.

Assume that air resistance is ignored.

Note:
The distance, h, of a falling object with initial vertical velocity of zero at time t is
h = (1/2)gt²
where
g = 9.8 m/s²

The initial vertical velocity of the supplies is 0 m/s.
It the time taken for the supplies to reach the ground is t, then
(50 m) = (1/2)*(9.8 m/s²)*(t s)²

Hence obtain
t² = 50/4.9 = 10.2041
t = 3.1944 s

The horizontal distance traveled at a speed of 100 m/s is
d = (100 m/s)*(3.1944 s) = 319.44 m

Answer: 319.4 m (nearest tenth)