# Two boats leave the port at the same time with one boat traveling north at 15 knots per hour and the other boat traveling west at 12 knots per hour. How fast is the distance between the boats changing after 2 hours?

##
So I draw a right triangle and label the sides as x and y and the hypotenuse as D (for distance). I'm guessing I'm going to have to use the pythagorean theorem and then take the derivative but I'm not quite sure of what to do with the 2 hours data...

Thank you!

So I draw a right triangle and label the sides as x and y and the hypotenuse as D (for distance). I'm guessing I'm going to have to use the pythagorean theorem and then take the derivative but I'm not quite sure of what to do with the 2 hours data...

Thank you!

The distance is changing at

By the pythagorean theorem, we have:

We now differentiate this with respect to time.

The next step is finding how far apart the two boats are after two hours. In two hours, the northbound boat will have done 30 knots and the westbound boat will have done 24 knots. This means that the distance between the two is

We cannot forget units, which will be knots per hour.

Hopefully this helps!

By signing up, you agree to our Terms of Service and Privacy Policy

The distance between the boats is changing at a rate of approximately 19.21 knots per hour after 2 hours.

By signing up, you agree to our Terms of Service and Privacy Policy

- How do you use linear approximation to estimate #root3( 64.1)#?
- How do you use Newton's method to find the approximate solution to the equation #tanx=e^x, 0<x<pi/2#?
- A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is minimum?
- What dimensions would you need to make a glass cage with maximum volume if you have a piece of glass that is 14" by 72"?
- How do you find the point on the curve #y=2x^2# closest to (2,1)?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7