Question

A boat crosses a river of width 229 m in which the current has a uniform speed of 0.756 m/s. The pilot maintains a bearing (i.e., the directicon in which the boat points) perpendicular to the river and a throttle setting to give a constant speed of 1.69 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.

Answer 1

Answer:

1.85 m/s

102.438 m

Explanation:

From vector motion

The resultant velocity

$R=\sqrt{0.756^2+1.69^2}\\\Rightarrow R=1.85\ m/s$

The magnitude of speed of the speed of the boat relative to a stationary shore observer is 1.85 m/s

The distance covered is 229 m

Time = Distance / Speed

$\text{Time}=\frac{229}{1.69}\\\Rightarrow \text{Time}=135.50\ s$

Distance = Speed of current × Time

Distance = 0.756×135.5 = 102.438 m

The boat will be 102.438 m from the initial position is the boat when it reaches the opposite shore