Saturday, November 29, 2014

Shoulda made that left turn at Andromeda

Here's another brachistochrone problem I was playing with:

You're coasting along in your space ship, when suddenly you miss a left turn. If you begin applying a constant-acceleration thruster immediately, how long will it take you to navigate your way back to the point where you missed the turn, reaching it with the same speed you had when you passed through it the first time, but with the direction of motion turned by 90 degrees from what it was originally?

One way to do it is to follow a 45-45-90 triangle:

Can it be done faster?

Second: What if you aren't required to revisit the origin after missing the turn, but instead all you have to do is get yourself traveling on the y-axis with vertical velocity at the original speed of motion?

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