Calculus 1 - Related Rates Question

Question

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 16 knots and ship B is sailing north at 24 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^2 = w^2 +n^2

2dd' = 2ww' + 2nn'

dd' = ww' +nn'

w=10+16(4)=74

w'=16

n =24(4)=96

n'=24

d^2 =74^2+96^2=14692

d= 121.21056

plug in the numbers and solve for d'=(74(16)+96(24))/121.21

=about 28.78 nautical miles per hour

= 28.78 knots = rate of change of distance between the ships