A boat crosses a river of width 152 m in which the current has a uniform speed o

Question

A boat crosses a river of width 152 m in which the current has a uniform speed of 1.97 m/s. The pilot maintains a bearing (i.e., the direction in which the boat points) perpendicular to the river and a throttle setting to give a constant speed of 3.03 m/s relative to the water. What is the magnitude of the speed of the boat relative to a stationary shore observer? Answer in units of m/s. How far downstream from the initial position is the boat when it reaches the opposite shore? Answer in units of m.

Explanation / Answer

Speed of the water = 1.97 m/s

Speed along the width = 3.03 m/s

Speed of boat (relative to the observer on shore) = sqrt(1.97 ^2 + 3.03 ^2) = 3.61 m/s

time to cross the width = 152/3.03 = 50.16 sec

distance traveled along the river during this time = 1.97 * 50.16 = 98.82 meter

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