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Problem of the Week

You might already know or have heard what the answer itself is to today's Problem of the Week, but try working it out for yourself!

Check below the break for my own way of finding the answer.

Did you figure this one out a different way? Had you been told this fact before, but without the reasoning behind it? Let us know in the comments!

The velocity of the cannonball has not been constrained. Might it be fired at a velocity greater than the escape velocity of the planet? But the planet is apparently infinitely large, so what is its escape velocity? The problem is very difficult. Is this why I failed my math courses?

ReplyDeleteThe cannonball's speed is fixed at some finite v. Since gravity is uniform, the gravitational potential at infinite height is infinite-there's no escape velocity. Don't overthink it too much; this is just a trajectory in idealized uniform gravity problem.

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