94 Chapt. 9 Momentum c) Write down the equation of motion again and solve for acceleration a as a function of time. Assume that mass change rate is a constant (which implies that thrust is constant) and solve for velocity as a function of time. HINT: Write mass as m ( t ) = m0 + ( dm/dt ) t , where m0 is initial mass. d) Assuming the gravity is negligible, use the result of part (c) to solve for the time t it take to reach escape velocity 11 . 2 km / s? Use the mass rate change found in part (b). By evaluating gt assess if gravity is in fact negligible? How much mass has the rocket lost in achieving escape velocity? 009 qfull 00800 3 5 0 tough thinking: multi-stage rocket Extra keywords: Fr-359-9-12, but highly modi±ed 7. Consider a fully-fueled, multi-stage rocket at rest in gravity-free space. There are I stages plus the payload which we will call stage I + 1, but the payload has no fuel. The mass of stage i is n i m , where m is the mass of the payload and n i is a dimensionless mass ratio:
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