Question

A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 22 ft/s.

At what rate is his distance from second base changing when he is halfway to first base?

At what rate is his distance from third base changing at the same moment?

Answer 1

when the runner is x feet from 1st base, his distance z from 2nd base is
z^2 = x^2 + 90^2
z dz/dt = x dx/dt
when x=45, z = 45√5, so
45√5 dz/dt = 45 * -22
dz/dt = -22/√5

now see what you can do with the distance to third base. (The right angle is at home plate)
Post your work if you get stuck.