Question

As a baseball player runs from second to third base, he is going 20 feet per second. What is the rate of change from the runner to home when he is halfway to third base? (The sides of a baseball field are 90 feet)

Answer 1

x^2 = (45-20*t)^2 + 90^2
2 x dx/dt = 2 *(45-20t) (-20)
at x=sqrt(45^2+90^2) when t = 0
2 (100.6) dx/dt = 90*-20
dx/dt = -8.94 ft/s