Question

can anyone help me with this question?

A baseball diamond is a square whose sides are 90 ft long. Suppose that a player running from second base to third base has a speed of 30 ft/sec at the instant when he is 20 ft from the third base. At what rate is the player’s distance from home plate changing at that instant.

Answer 1

let the distance from 3rd base be x. Then the distance z from home is

z^2 = 90^2 + x^2
so, to find dz/dt,

2z dz/dt = 2x dx/dt

So, find z when x=20, then plug in dx/dt and x.