Question

A boat crosses a river of width 226 m in which the current has a uniform speed of 1.77 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 2.54 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

3.1 m/s

Step-by-step explanation:

Speed of current = 1.77 m/s =
`v_c`

Speed of boat relative to the water = 2.54 m/s =
`v_b`

Speed observed by someone on the shore

From the vector analysis. The required vector would be the length of the hypotenuse. The hypotenuse is found from the Pythagoras theorem.
`v_c` and
`v_b` are the two sides of a triangle while v is the hypotenuse.

`v=√(v_c^2+v_b^2)\\\Rightarrow v=√(1.77^2+2.54^2)\\\Rightarrow v=3.1\ m/s`

Speed observed by someone on the shore is 3.1 m/s