Question

The boat is headed with a velocity of 18 meters/seconds toward the west with respect the water in a river. If the river is flowing with a velocity of 2.5 meters/seconds in the same direction as the boat. What would be the magnitude of the boats velocity?

Answer 1

To find the boat's resultant velocity with respect to the shore, sum the velocity of the boat relative to the water (18 m/s) and the river's velocity (2.5 m/s), which are both westward. The resultant velocity is 20.5 m/s.

Step-by-step explanation:

Calculating Resultant Velocity of a Boat

When a boat is moving through a river, its total velocity with respect to the shore (resultant velocity) is the vector sum of the velocity of the boat relative to the water and the velocity of the river. If the boat heads straight across the river, its velocity is perpendicular to the flow of the river, and we can calculate the resultant velocity using the Pythagorean theorem. However, in this scenario, both the boat's velocity and river's velocity are in the same westward direction.

The person asks about the boat's velocity with respect to the water, which is 18 m/s, and the river's velocity, which is 2.5 m/s, both in the same direction.

Hence, the magnitude of the boat's resultant velocity is the algebraic sum of both speeds since they are in the same direction.

The boat's resultant velocity with respect to the shore would therefore be:

Velocity of the boat relative to the river + velocity of the river = 18 m/s + 2.5 m/s

= 20.5 m/s

This resultant velocity represents the boat's speed with respect to a stationary observer on the shore.