A rocket of total mass 3180 kg is traveling in outer space with a velocity of 11

Question

A rocket of total mass 3180 kg is traveling in outer space with a velocity of 110 m/s. To alter its course by 25.5 °, its rockets can be fired briefly in a direction perpendicular to its initial motion. Part A If the rocket gases are expelled at a speed of 1900 m/s how much mass must be expelled? [Hint: Use a velocity triangle to relate the initial velocity of the rocket to the additional velocity component needed to alter its course by 25.5 °] Express your answer with the appropriate units. Vale kg

Explanation / Answer

Let the initial speed be vo

Change in velocity, v' = vo tan25.5

Using law of conservation of momentum  

(M - m) v' = mv

(3180 - m) (110 tan25.5) = m (1900)

(3180 x 52.467) - 52.467m = 1900m

m = 85.45 kg

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