# Spaceship rotation problem

A 20-meter-long spaceship is drifting in space, and is in the orientation shown below left, initially not spinning at all. The pilot needs to get the spaceship turned around 180 degrees, with the positions of the nose and tail switched around, as shown below right. To accomplish this, he fires a pair of small identical rocket engines (shown in red, labeled "A" and "D") at the same time. Each engine is located at one of the ends of the spacecraft, and each exerts a constant force of 5000 N on the spacecraft, in direction perpendicular to the long axis of the spacecraft. The directions of the forces from engines A and D are opposite to each other. The pilot turns engines A and D on for just 1 second, and then turns them off. At this point the spacecraft will have acquired some rotation. When the spacecraft has turned around almost a complete half-circle, the pilot turns on the engines labeled "B" and "C". Again, engines B and C each exerts an equal and opposite constant force of 5000 N perpendicular to the long axis of the spacecraft, and each is turned on simultaneously for 1 second and then turned off. The end result is that the spacecraft will now once again be at rest, but turned around 180 degrees from where it started.

Assume that the spacecraft can be approximated as a long, uniform thin rod, ignoring the irregularities in shape at the nose and the tail. How long does it take the pilot to complete this 180-degree turnaround maneuver, starting from rest and ending at rest?

(see diagram in attached file)

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#### Solution Preview

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A 20-meter-long spaceship is drifting in space, and is in the orientation shown below left, initially not spinning at all. The pilot needs to get the spaceship turned around 180 degrees, with the positions of the nose and tail switched around, as shown below right. To accomplish this, he fires a pair of small identical rocket engines (shown in red, labeled "A" and "D") at the same time. Each engine is located at one of the ends of the spacecraft, and each exerts a constant force of 5000 N on the spacecraft, in direction perpendicular to the long axis of the spacecraft. The directions of the forces from engines A and D are opposite to each other. The pilot turns engines A and D on for just 1 second, and then turns them off. At this point the spacecraft will have acquired some rotation. When the spacecraft has turned around almost a complete half-circle, the pilot turns on the engines labeled "B" and "C". Again, engines B and C each exerts an equal and opposite constant force of 5000 N perpendicular to the long axis of the spacecraft, and each is turned on simultaneously for 1 second and then turned off. The end result is that the spacecraft will now once again be at rest, but turned around 180 degrees from where it started.

Assume that the spacecraft can be approximated ...

#### Solution Summary

This solution calculates how long it takes for a pilot to complete a 180-degree turnaround maneuver, starting from rest and ending at rest