Question

Rate of Change Problem!! Please help :/ At noon, shop A is 100km west of ship B. Ship A is sailing south at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between ships changing at 4:00 PM?

Answer 1

From the diagram to find distance d:
d = sqrt(100^2 + (A+B)^2)

A = 35t
B = 25t

d = sqrt(100^2 + 60^2*t^2) = 10sqrt(100+36t^2)
to find rate dd/dt, take derivative using chain rule
u = 100+36t^2
du = 72t

dd/dt = d/dt (10sqrt(u))*du

dd/dt = 5/sqrt(u)*72t = 360t/sqrt(100+36t^2)

Now evaluate when t=4