The velocity v (in feet per second) of a rocket whose initial mass (including fuel) is m is given by

where u is the expulsion speed of the fuel, r is the rate at which the fuel is consumed, and g = -32 feet per second per second is the acceleration due to gravity. Find the position equation for a rocket for which m = 50,000 pounds, u = 12,000 feet per second, and r = 400 pounds per second. What is the height of the rocket when t = 100 seconds? (Assume that the rocket was fired from ground level and is moving straight upward.)

Transcribed Image Text:

v = gt + u ln V m m - rt' t< m