# Need help with a Calculus III / Related Rates Problem — How to Solve It

A child walks due east on the deck of a ship at 1 miles per hour. The ship is moving north at a speed of 9 miles per hour.

Find the speed and direction of the child relative to the surface of the water.

Speed = __ mph

The angle of the direction from the north = ___ (radians)

The last time I solved a problem like this was last summer, it looks like a "Related Rates" problem; so, I just need a refresher if anyone could care to help. Thank you very much.

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Almost all related rates problems amount to a use of the chain rule dy/dt = (dy/du)(du/dt). Of those three factors in the chain rule equation, typically you'll know one of them right off the bat, you'll find a formula for a second one from some geometric fact, and then solve for the third. – Jesse Madnick Jan 12 '11 at 8:22

## 1 Answer

Hint: You have a right angle triangle, 1 mi/hr in the easterly direction and 9 mi/hr in the northerly direction. The total speed comes from Pythagoras and the angle from trigonometry.

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