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

Given that,

total mass, M = 3180 kg

initial velocity of rocket, vr =110 m/s

speed of expelled gas, vg = 1900 m/s

Let, mass of expelled gas = mg

final speed of rocket = vf

Final mass of rocket = (M - mg)

From conservation of momentum in x direction,

M*vr = (M - mg)*vf*cos(25.5) .......(1)

From conservation of momentum in y direction,

mg * vg = (M - mg)*vf*sin(25.5) ........(2)

From equation (1) and (2),

mg * vg / M*vr = tan(25.5)

mg * 1900 = 3180*110*tan(25.5)

mg = 87.8 kg

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