A 199-m-wide river flows due east at a uniform speed of 1.9 m/s. A boat with a s

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A 199-m-wide river flows due east at a uniform speed of 1.9 m/s. A boat with a speed of 7.8 m/s relative to the water leaves the south bank pointed in a direction 30° west of north.

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Explanation / Answer

Solution-

The west component of the boat's velocity is 7.8*sin(30) = 3.9 m/s

and the North component is 7.8*cos(30) = 6.75 m/s

So the net velocity of the boat relative to the ground is 3.9 - 1.9 = 2.00m/s West and 6.75 m/s N

Therefore the magnitude is sqrt(2.00^2 + 6.75^2) = 7.04 m/s

and the angle is arctan(-2.00/6.75) = -16.5o

The time to cross = x/t = 199/6.75m/s = 29.48s

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