At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west

Question

At noon, ship A is 50 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 22 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.)

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

let t hours be some time after noon
(so 5:00 pm is t=5)

so you have a right angled triangle with a vertical of 22t nautical miles and a horizontal of (17t + 50) nautical miles

let the distance between them, or the hypotenuse, be s nautical miles

s^2 = (22t)^2 + (17t+50)^2
2s(ds/dt) = 484*2 t + 34(17t+50)

so when t=5
s^2 = 484(5^2) + 135^2
s = ?30325

ds/dt = (484x2x5 + 34(135))/(2?30325)
= 27.075

so at 5:00 pm the distance between them is changing at 27.075 knots

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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