At noon, ship A is 20 nautical miles due west of ship B.

Question

At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 22 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 4 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

Answer 1

D = sqrt( A^2 + B^2)

dD/dt = (1/2)(A^2 + B^2) ( 2A dA/dt + 2B dB/dt)

= ( A dA/dt + B dB/dt)/ sqrt( A^2 + B^2)

After 4 hours, B=20 + 22*4 = 20 + 88 = 108 and A = 16*4 = 64

D = sqrt( 108^2 + 64^2) = sqrt(15760) = 153.5388.....

Finally

dD/dt = ( 64 * 16 + 108*22)/153.5388 = 27.083252-