Question

A boat crosses a river of width 161 m in which the current has a uniform speed of 1.09 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 2.77 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.

Answer 1

|v|=2.98m/s

Step-by-step explanation:

In order to solve this problem we must first draw a diagram that will represent the situation. (See picture attached)

In this case the boat is being dragged by the river while it has a given velocity relative to the water and perpendicular to the flow of the river. We can take these velocities as vectors so we can add them up:

`|v|=\sqrt{(1.09m/s)^(2)+(2.77m/s)^(2)}`

which yields:

|v|=2.98m/s

so an observer that is stationary on the shore will se the boat having a speed of 2.98m/s.