Related rates

1. Oct 23, 2007

bondgirl007

1. The problem statement, all variables and given/known data

Ship A travels at 10 knots on a due north course and passes a buoy at 8am. Ship B, travelling on a due east course passes the same buoy at 10am. How fast are the ships separating at 12 am?

2. Relevant equations

3. The attempt at a solution

I'm not familiar with knots and don't know what knots are in km/h. Also, how fast is Ship B traveling then?

2. Oct 23, 2007

HallsofIvy

Staff Emeritus
Why would you want to change to km/h? The problem doesn't require that you do. A "knot" is, as the problem implies, a unit of speed (it is one nautical mile per hour but you don't need to know that either to do the problem- just give the answer in knots).

However, in your second question you hit on the difficulty. You can't possibly answer this without know how fast ship B is traveling and apparently that is not given.

3. Oct 23, 2007

bondgirl007

Would it be possible to find the speed of B by comparing the time it takes for both A and B to pass the buoy?

4. Oct 23, 2007

stewartcs

I don't see how you could. You know nothing of the distanced travelled (which is what you are really after in the first place).

5. Oct 23, 2007

bondgirl007

The time is 4 hours so can't you multiply that by 10 knots to find the distance of A?

6. Oct 23, 2007

stewartcs

Sure, but that won't tell you the speed of B. It will tell you the distance travelled by A which is one part of the problem. If you knew the speed of B, you could take the same approach and find the distance travelled by B (B's speed x 2 hours).

Then you could use that information to find the rate of change between the two by using the Pythagorean theorem (differentiating it of course).

Last edited: Oct 23, 2007