Astronaut launches bowling ball

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A 100 kg astronaut carries a launcher loaded with a 10 kg bowling ball; the launcher and the astronaut’s spacesuit have negligible mass. The astronaut discovers that firing the launcher results
in the ball moving away from her at a relative speed of 50 m/s.

The astronaut in the previous situation is now moving at 10 m/s (as measured in a certain frame
of reference). She wishes to fire the launcher so that her velocity turns through as large an angle
as possible (in this frame of reference). What is this maximum angle? (Hint: a diagram may be
useful.)

The answer is 27 degrees. I do not know how. I think she must fire the ball perpendicularly to her velocity, but I instead got 29 degrees as my answer. Help?

  • Astronaut launches bowling ball -

    The maximum angle actually does not occur when she fires the ball perpendicularly to her velocity. It occurs when the angle between the velocity from the launcher and the resultant velocity are at 90 degrees to each other. The impulse of the astronaut is about 455 Ns. Therefore, the velocity given by the ball is 4.55 m/s. sin angle = 4.55/10 so the angle is 27 degrees.

  • Astronaut launches bowling ball -

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