Question

An emergency relief airplane is dropping a care package to people on a small island. The plane is flying with a velocity of v0 = 176 km/h at an altitude of h = 393 m.

If the package must land on the island, at what horizontal distance D from the plane to the island should the package be dropped?

Answer:

2.
What is the magnitude of the final velocity of the package the instant before it hits the ground?

Answer 1

use

Time taken for an object to fall distance :

$\ t =\ \sqrt {\frac{2d}{g}}$

time taken by package to fall 393 meters = 8.95 seconds

initial velocity in x direction of the package = 176 km/h = 48.8889m/s

hence horizontal distance needed = 48.9 * 8.95 = 437 meters

for velocity use

Instantaneous velocity of a falling object after elapsed time :

Vy = 9.8 * 8.95 = 87.71 m/s in x direction = 48.88 m/s total velocity = ( x2 + y2)^0.5 =100 m/s