Question

A person stands 800ft away from a rocket launching pad. The rocket is launched vertically and keeps a velocity of 200 ft/s. How fast is the distance between the observer and the rocket changing when the rocket is 600ft above the ground?

Answer 1

120 ft/2

Explanation:

Let the vertical distance of the rocket be y.

Let the distance between the observer and the rocket be z.

The horizontal distance between the observer and the rocket is 800 ft.

When the rocket is 600 ft above ground, y = 600.

800² + 600² = z²

z = 1000

z² = 800² + y²

Differentiate with respect to time.

2zz' = 2yy'

z' = (2yy')/(2z)

z' = yy'/z

z' = (600)(200)/1000

z' = 120000/1000

z' = 120

Answer: 120 ft/s