Calculus question

Question

At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 7 PM?

The distance is changing at ________________  knots.



(Note: 1 knot is a speed of 1 nautical mile per hour.)

Answer 1

Well suppose position is measured on a coordinate system with B's position at noon at the origin.

Then at noon A is at (-40,0), B is at (0,0).

t hours after noon, A is at (-40 - 17t, 0) B is at (0, 16t)

If s(t) is distance between them then by distance formula

s² = (-40 + 17t)² + (16t) ²

You want to know ds/dt when t = 7

----------------------------------------------------------------------------------------------------------------

2s ds/dt = 2 (-40 + 17t) (17) + 2 (16t) (16)

You can find s (7) using the equation above .

Then you can find ds/dt (7)