Question

A package of supplies is to be dropped from an airplane so that it hits the ground at a designated spot near some campers. The airplane, moving horizontally at a constant velocity of 140 km/hr, approaches the spot at an altitude of 0.5 km above level ground. Having the designated point in sight, the pilot prepares to drop the package. How far horizontally from the drop point should the pilot release the package? What is the location of the plane when the package hits the ground?

Answer 1

392.8 m

Step-by-step explanation:

Horizontal velocity is 38.89 m/s

Vertical distance y =0.5 km = 500 m

First calculate the time in which the package will hit the ground.

Use the second equation of motion

`y = u t + 0.5 at^2`

`500 = 0 + 0.5 (9.8) t^2`

t =10.1 s

Horizontal distance covered in the same time is

x = ut = (38.89) (10.1) = 392.8 m

The plane will cover the same horizontal distance in the time in which the package hits the ground.

Answer 2

s = ut + 0.5 at^2

0.5 ( 1000) = 0 (t) + 0.5 (9.81)t^2

t = root | 1000/9.81

For horizontal component, use :

s = (140 x 1000 ) / (60 x 60) x root|1000/9.81
= 392m

hope this helps