Question:

The height of a rocket, launched from the ground, is given by the function y = 30 t − 5 t 2 , where y is in meters and t is in seconds. An observer is sitting at ground level a distance d from the launch point. If r is the distance between the observer and where the rocket is, show that d r d t = ( 30 t − 5 t 2 ) ( 30 − 10 t ) √ ( 30 t − 5 t 2 ) 2 + d 2 . Show all your work.