Question
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)
Answers
Scott
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
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