Related Rates Softball Diamond

Question

A softball diamond has the shape of a square with sides of 60 feet. If a player is running from 2nd to 3rd base at 24ft./sec., at what rate is the distance between the runner and home plate changing when she is 20 feet from third base?

Answer 1

If x is the distance left from 2nd to 3rd, dx/dt = -24 ft/s, x = 20 ft. From the right triangle with side 60 (from 3rd to home) and x, we get the hypotenuse of D = sqrt(60² + x²) (This is the distance to home plate)

Take dD/dt = x dx/dt /sqrt(x²+ 3600)

Plug in all the values for the right-hand-side.

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