Suppose a player is running from first to second base 20ft/s. Find rate at which distance from home plate is changing when the player is 30ft away from 2nd base?(home plate to 1st and 3rd base is 90ft)

Answer 1

bases are arranged in a square, 90 ft on a side

f = home to 1st , s = distance from 1st

distance to home plate (p)
... p^2 = f^2 + s^2 = 90^2 + 60^2

2 p dp/dt = 2 s ds/dt

dp/dt = (s / p) ds/dt