Question

A baseball player is running from the at 20 ft/sec. At what rate is his distance from the home plate changing when he is 30 ft from the third base. The baseball diamond is a square 90 ft on a side.

Answer 1

draw a diagram. I assume he is running from 2nd base to 3rd base, other wise it is trivial.

The distance z when he is x ft from 3rd base is

z^2 = x^2 + 90^2
2z dz/dt = 2x dx/dt