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

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 17 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.) Note: Draw yourself a diagram which shows where the ships are at noon and where they are "some time" later on. You will need to use geometry to work out a formula which tells you how far apart the ships are at time t, and you will need to use "distance = velocity * time" to work out how far the ships have travelled after time t.

Explanation / Answer

First we find an equation to represent both ships and the distance between each. A is moving 22knots west and B is moving 17knots north. D will be the distance between the two. Drawing it, you'll notice that it creates a right triangle. So we use the Pythagorean Theorm: D^2 = A^2 + B^2 Differentiate in relation to time: 2D (dD/dt) = 2A (dA/dt) + 2B (dB/dt) Now we must find all of our variables. A = time(speed) + original distance = 6(22) + 10 = 142 B = 6(17) + 0 = 102 D = v(A^2 + B^2) = 174.837 dA/dt = 22 dB/dt = 17 dD/dt = how fast the distance is changing Plug in all your variables and solve for (dD/dt): 2D (dD/dt) = 2A (dA/dt) + 2B (dB/dt) 2(174.837) (dD/dt) = 2(142)(22) + 2(102)(17) 349.674 (dD/dt) = 9716 dD/dt = 9716 / 349.674 dD/dt = 27.786 knots At 6pm the distance between the ships is changing at the speed of 27.786 knots

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.