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Hello.
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In this problem we have an astronaut that is standing on the surface of the moon and then he fires a gun such that the bullet is fired initially horizontally.
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And we are asked about how fast should this bullet be if we needed this bullet to keep going in a circle around the moon and turns back to its original location.
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This problem depends on the concept of the equivalence of the gravitational acceleration and the centributal or the radial acceleration.
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They are the same in this type of problems.
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So here, we simply need to get the speed that is required to satisfy the following equation of centributal acceleration.
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In this problem, we are asked to consider the gravitational acceleration of the moon to be 163.
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Of the moon's of the earth is gravity.
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So it's around 1 .63 meters per second squared.
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And the second thing that we need to know that the radius of the moon is 1 ,737 kilometers approximately.
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So from this equation, in order to get the v, we just need to take the square root of a times r, where a is the gravitational acceleration of the moon, and r is the radius of the moon...