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

t <
V3 — gt + и In
т — rt'
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Transcribed Image Text

m m t < r V3 — gt + и In т — rt'