At a distance of 4,000 ft from the launch site, a spectator is observing a rocket being launched. If the rocket lifts off vertically and is rising at a speed of 600 ft/sec when it is at an altitude of 3,000 ft, how fast is the distance between the rocket and the spectator changing at that instant?Solution) Distance=s=√(4000^{2}+h^{2}), rate of change of distance=ds/dt=(ds/dh)(dh/dt)=(d(√(4000^{2}+h^{2})/dh)(dh/dt),dh/dt=600 ft/sec