At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 20 knots and ship B is sailing north at 25 knots. How fast (in knots) is the distance between the ships changing at 7 PM? (Note: 1 knot is a speed of 1 nautical mile per hour).
2007-11-03 09:55:59 · 2 answers · asked by alawrence108 1 in Science & Mathematics ➔ Mathematics
D = sqrt((20 +20t)^2 + (25t)^2)
D = sqrt(400 + 800t + 400t^2 +625t^2)
D = sqrt(400 +800t + 1025t^2)
D = 5sqrt(16 +32t + 41t^2)
dD/dt = 5(32+82t)/(2sqrt(16 +32t + 41t^2))
dD/dt = 5(32 +82*7)/(2sqrt(16+32*7 +41(7)^2)
dD/dt = 3030/94.85 = 31.95 knots
2007-11-03 10:18:27 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
I suggest you draw a picture of what is going on so you can see what you are trying to find. It sounds like you are going to have a right triangle if you draw it out to find the distance you will need to use a^2+b^2=c^2. Make sure your units are all correct. You probably have formulas for position and velocities. v=dx/dt
2007-11-03 10:01:41 · answer #2 · answered by Anonymous · 0⤊ 0⤋