Question

A river flows at a speed of 4.60 m/s. A boat, capable of moving with a speed of 5.87 m/s in still water, is rowed across the river at an angle of 59.0° to the river flow. Calculate the resultant velocity with which the boat moves.

A. 6.67 m/s
B. 3.82 m/s
C. 7.14 m/s
D. 4.19 m/s

Answer 1

The resultant velocity with which the boat moves is approximately A) 6.67 m/s.

Step-by-step explanation:

To calculate the resultant velocity with which the boat moves, we can use vector addition. The boat's velocity can be broken down into two components: one parallel to the river flow and one perpendicular to it. The parallel component of the boat's velocity is given by Vparallel = Vboat * cos(θ), where Vboat is the boat's speed in still water and θ is the angle between the boat's direction and the river flow.

The perpendicular component of the boat's velocity is given by Vperpendicular = Vboat * sin(θ).

The resultant velocity of the boat is then calculated as Vresultant = sqrt(Vparallel2 + Vperpendicular2).

Plugging in the given values: Vboat = 5.87 m/s and θ = 59.0°, we can calculate the resultant velocity to be approximately 6.67 m/s.