Problem 3.41: Crossing the River, II. A river flows due south with a speed of 1.

Question

Problem 3.41: Crossing the River, II.

A river flows due south with a speed of 1.50m/s . A man steers a motorboat across the river; his velocity relative to the water is 4.40m/s . The river is 800m wide.

Part A

In which direction should the motorboat head in order to reach a point on the opposite bank directly east from the starting point? (The boat's speed relative to the water remains 4.40m/s .)

Part B

What is the velocity of the boat relative to the earth?

Part C

How much time is required to cross the river?

Explanation / Answer

If the boat is heading angle t north of east, the component of its velocity to the north must equal the velocity of the river to the south:
4.2 sin(t) = 2.0
t = 28.4 deg.

The velocity of the boat relative to earth is:
4.2 cos(t)
= 3.69 m/s. due E.

The crossing time is:
800 / 3.69
= 217 sec.
= 3m. 37s.

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