A river flows due south with a speed of 2.10 m/s. A man steers a motorboat acros

Question

A river flows due south with a speed of 2.10 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4.50 m/s. The river is 600 m wide.

1. 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 4.50) answer needs to be in degrees north of east.

2. What is the velocity of the boat relative to the earth? m/s is the units

3. How much time is required to cross the river? s (sec) is the units

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: as destination directly east from the starting point 4.5 sin(t) = 2 t = 26.4 deg. The velocity of the boat relative to the earth is: =4.5 cos(t) ( as 4.5 sin(t) is cancelled by river speed) = 4.0312 m/s. due E. The crossing time is: 600 / 4.0312 = 148.84 sec.

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