A model rocket consisting of a 61.3-g chassis and a 30.5-g engine is taken on an

Question

A model rocket consisting of a 61.3-g chassis and a 30.5-g engine is taken on an interstellar mission and fired in outer space. The engine produces 4.85 N of thrust while expending 14.0 g of fuel at a constant rate during a 2.01-s burn. (Assume the mass of the engine includes the mass of the fuel.) (a) What is the average exhaust speed of this rocket's engine? (b) If the rocket starts from rest, what is its final velocity? (Assume the thrust to be in the positive direction. Indicate the direction with the sign of your answer.)

Explanation / Answer

(a) average exhaust speed of this rocket's engine

Assuming a constant rate of mass consumption,

dm/ dt = m/ t

. F = ve* dm /dt ,

ve = F t /m

=4.85*2.01/14

=696.32m/s

(b) If the rocket starts from rest

?v = ve* ln ( mi /mf ) .

In this case, mi = M + m0 and mf = M + m0 ? m.

vf = F t /m ln ( M + m0/ (M + m0 ? m))

=696.32*ln(61.3+30.5/(61.3+30.5-14))

=114.66m/s

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