Question

An observer is located on the ground 6 kilometers from the point where a space shuttle is launched (vertically). When the shuttle is 8 kilometers high, it is travelling at 500 kilometers per hour. Determine, for that moment, the rate at which the distance between the observer and the shuttle is changing.

Answer 1

draw a diagram. The distance from the observer to the shuttle when the height is y, is

d^2 = 6^2 + y^2

2d dd/dt = 2y dy/dt

when y=8, d=10 so

20 dd/dt = 2(8)(500)
dd/dt = 400 km/hr