# Related Rates

• Nov 1st 2008, 10:53 AM
gearshifter
Related Rates
At noon, ship A passes 7 km WEST of a harbour, heading due NORTH at 9 km/h. At 9 a.m., ship B had left the harbour, sailing due NORTH at 6 km/h. Give an expression for d, the distance between the two ships, in terms of t, the number of hours after noon.
• Nov 2nd 2008, 12:11 AM
earboth
Quote:

Originally Posted by gearshifter
At noon, ship A passes 7 km WEST of a harbour, heading due NORTH at 9 km/h. At 9 a.m., ship B had left the harbour, sailing due NORTH at 6 km/h. Give an expression for d, the distance between the two ships, in terms of t, the number of hours after noon.

Use a coordinate system with the harbour at (0, 0), the positive x-axis pointing East and the positive y-axis pointing North.

Then the position of ship A is:

$\displaystyle A(-7, 9t)$ and the position of ship B is:

$\displaystyle B(0, 6(t+3))$

Now use the distance formula:

$\displaystyle d=\sqrt{(-7-0)^2+(9t-6(t+3))^2} = \sqrt{9t^2-108t+373}$