Thread: 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.

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:

and the position of ship B is:



Now use the distance formula: