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Title: GR8677.061
Post by: conantee on January 06, 2010, 11:45:11 AM
Question 61-62
The equation of motion of a rocket in free space can be written
m \frac{dv}{dt} + u \frac{dm}{dt} = 0
where m is the rocket's mass, v is its velocity, t is time, and u is a constant.

61. The constant u represents the speed of the
(A) rocket at t=0
(B) rocket after its fuel is spent
(C) rocket in its instantaneous rest frame
(D) rocket's exhaust in a stationary frame
(E) rocket's exhaust relative to the rocket


Title: Re: GR8677.061
Post by: conantee on October 11, 2010, 11:24:50 AM
This is a free lunch if you look closely to the fact that u is constant. Actually, it implies that it is constant throughout the motion. Another point is that this speed is attached with the change of rocket mass, which is rocket's exhaust. Combining this two facts together, the answer should be (E). The rocket's exhaust in a stationary frame is unlikely to be constant since the rocket is moving with acceleration - as far as we concerned.

The correct answer is (E). 55 of 100 people answer this question correctly.