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Unformatted text preview: Physics 325, Fall 2010 Prof. Susan Lamb Homework Assignment #3 Solutions 1a) From class, we have v ( t ) = v + u ln m m for a rocket without gravity, which applies here because gravity is balanced by the normal force in the vertical direction, and were ignoring air resistance. The initial speed v = 0. Call v 2 the maximum speed. When the rocket car has speed v 2 , it starts decelerating back to zero speed. Call m 2 the total mass of the rocket car when it has speed v 2 . Then v 2 = u ln m m 2 The final speed is zero, and we reverse the sign of u to slow the car down from v 2 to zero, and the mass goes from m 2 down to m 1 : 0 = v 2- u ln m 2 m 1 Putting these two relations together we get u ln m 2 m 1 = u ln m m 2 m m 2 = m 2 m 1 m 2 = m m 1 1b) We need to compute two functions for v ( t ) because of the reversal of the rocket engines. One calculation we need to do for t < T , where T is the time at which the engines reverse, and the other for t > T ....
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