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How much farther a person can jump on the Moon?

Determine how much farther a person can jump on the Moon as compared to the Earth if the take-off speed and angle are the same. The acceleration due to gravity on the Moon is one-sixth what it is on Earth.

Solution Preview

Let's denote the horizontal position by x and the height by y (both relative to the take-off point). Suppose we take-off at time t = 0 with a speed in the y direction of v_{y} and the speed in the x direction of v_{x}.
Then the height as a function of time is:

y = v_{y}t ...

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