Answer to Question #256542 in Physics for megs

Question

A graduate student runs a model space shuttle launch test to test a potential new rocket booster design. The 13 kg rocket booster is used to help launch the 182 kg space shuttle. At the moment before the booster detaches from the shuttle, the velocity of the shuttle and booster is 69 m/s [E 65° up]. When the booster detaches from the shuttle, the space shuttle has a velocity of 60 m/s [E 75° up]. Determine the velocity and direction of the booster right after it detaches from the shuttle.

Note: For this question, please include both the velocity and direction on your written solution. There is no need to place your answer in the answer box for this problem.

Answer 1

The momentum is conserved along both axes:

$$x: (m+M)v\cos\theta=Mu\cos\phi+m\nu\cos\alpha,\\ y: (m+M)v\sin\theta=Mu\sin\phi+m\nu\sin\alpha,\\\space\\ \tan\alpha=\frac{(m+M)v\sin\theta-Mu\sin\phi}{(m+M)v\cos\theta-Mu\cos\phi},\\\space\\ \alpha=30°,\\ \nu=254\text{ m/s}.$$