A baseball diamond has the shape of a square with sides 90 feet long (see figure).

Question

A player running from second base to third base at a speed of 25 feet per second is 21 feet from third base. At what rate is the player's distance from home plate changing? (Round your answer to two decimal places.)

Answer 1

Related rate problem:

1) Connect x and d: d = sqrt(90²+ x²)

2) We know dx/dt = -25 ft/s and x = 21 ft at moment of interest

30 Differentiate eqn (1) in terms of t and apply chain rule:

dd/dt = 1/2 (90²+x²)^-1/2(2x) dx/dt

4) Substitute in to find dd/dt at x = 21 ft. (Note that you will get a negative rate)