A space shuttle of inertia m is attached to a booster rocket that has an inertia

Question

A space shuttle of inertia m is attached to a booster rocket that has an inertia nine times greater. This system is moving at a speed of 850 m/s in outer space, as seen by observers in a nearby space station. Then explosive bolts are detonated, separating the shuttle from the rocket and thrusting the shuttle forward at a speed of 200 m/s relative to the rocket. Suppose that the shuttle and the rocket are initially moving in the positive i^ direction.

a) What is the velocity of the rocket right after the explosion?

b) What is the velocity of the shuttle right after the explosion?

Explanation / Answer

a) R=Rocket , S= Shuttle, G= ground

VSR = VSG – VRG

VSG = VSR + VRG -----------------(1)

Use law o conservation of linear momentum

Pf - Pi =0

[mS* VSG - mR* VRG] – [(mS+mR)*V] = 0

[ mS*(VSR + VRG) - mR* VRG] - [ (mS+mR)*V] =0

[m*(VSR + VRG) - 9m*VRG] – [(m+9m)*V] =0

[m*VSR + mVRG - 9m*VRG] – [(m+9m)*V] =0

[m*VSR - 8m*VRG] – [(m+9m)*V] =0

[ VSR -8*VRG] – [10*V] =0

[200 -8*VRG] – [10*850] =0         => VRG = 1037.5 m/s

b) VSG = VSR + VRG = 200+ 1037.5 = 1237.5 m/s

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