Question

You are attempting to row across a stream in your rowboat. Your paddling speed relative to still water is 3.0 m/s but assume that the stream flows east at 4.0 m/s. Determine how far downstream of your starting point you will finally reach the opposite shore if the stream is 6.0 meters wide.

Answer 1

By using vector addition and the principles of kinematics in Physics, we calculate that the rowboat will reach the opposite shore of the stream 8 meters downstream from the starting point.

Step-by-step explanation:

The question involves a mixture of kinematics and vectors, which are topics in Physics. When the boat attempts to cross a stream that has a flow velocity to the east (perpendicular to the desired direction of travel), the boat's actual path will be the result of the vector addition of the boat's velocity and the stream's velocity. To analyze this, we can break the problem into a right-angled triangle with the boat's velocity vector as one side and the stream's velocity vector as the hypotenuse.

To solve for the distance downstream you will be once you reach the opposite side, use the following steps:

1. Determine the time it takes to cross the river, which is the width of the river divided by the rowing speed perpendicular to the current (since you're crossing straight to the other side at 3.0 m/s): Time = Width / Speed = 6.0 m / 3.0 m/s = 2 s.
2. Calculate the distance drifted downstream using the speed of the current and the time calculated above: Distance = Stream Speed * Time = 4.0 m/s * 2 s = 8 m.

You would end up 8 meters downstream from your starting point on the opposite shore.