Question

At 3 P.M, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 7 P.M.? (Round your answer to one decimal place.)

Answer 1

Call O the initial location of ship B. A is sailing toward O and B is sailing away from O. Call x the distance between ship A and O at time t and y the distance between point O and B. Since x is decreasing and y is increasing, dx/dt = -35, dy/dt = 25.

Call S the distance between Ship A and ship B at time t, we have
S^2 = x^2 + y^2
and the change of S at time t is
2S (dS/dt) = 2x (dx/dt) + 2y (dy/dt) or
dS/dt = [x (dx/dt) + y (dy/dt)]/S
At 7pm, or 4 hours later, x = 10, y = 100, and S = sqrt (10^2 + 100^2) = 100.5
Finally,
dS/dt = [10 (-35) + 100 (25)]/100.5 = (-350 + 2500)/100.5 = 21.39 km/h

Answer 2

thanks a lot :)