Ships in nautical miles

Question

At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 15 knots and ship B is sailing north at 17 knots. How fast (in knots) is the distance between the ships changing at 5 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

Answer 1

Hi Joey H.,

How fast the distance is changing between the ships is the speed between them.

Use vectors with v_w equal to the velocity in the west direction, v_n the velocity in the north direction, and v_b the velocity between them.

v_w = -15i (west in the negative x-direction)

v_n = 17j (north in the positive y-direction)

v_b = v_n - v_w = 15i + 17j (where v_w + v_b = v_n)

The speed between them is the magnitude of |v_b| = √(15² + 17²) = 22.67 knots.

As you can see, you could have just used the speeds, as they form a right triangle, and just used the Pythagorean theorem.

The initial distance of 10 nautical miles would come into play if we were finding the distance between them. (d_w = |v_w|*t + 10 and d_n = |v_n|*t)

I hope this helps, Joe.