How Does Relative Velocity Affect a Swimmer's Path Across a River?

[confusedguy87]

A swimmer heads directly across a river, swimming at 1.6m/s relative to the water. She arrives at a point 40m downstream from the point directly across the river, which is 80m wide.

A) What is the speed of the river current?
B)What is the swimmer's speed relative to the shore?
C)In what direction should the swimmer head in order to arrive at the point directly opposite her starting point?


Can someone guide me in a starting point? I am really confused on the whole "relative velocity" topic. All those "relative" to this and to that gets me confused.
Can someone help me break down what the problem really is saying?

 

[Kurdt]

Part A is similar to projectile motion. You need to take components of motion. You know the swimmers velocity across the river and can work out how fast it would take to reach the other side if the river was still. Then you can work out how fast the river must move to sweep her forty metres off course in the same time.

 

[baba89]

Sure! Let's break down the problem step by step.

First, we are given that there is a swimmer in a river. The swimmer is moving at a speed of 1.6m/s relative to the water. This means that the swimmer is moving at a constant speed of 1.6m/s in the direction of the water flow. It is important to note that this speed is relative to the water, not to the shore or any other reference point.

Next, we are told that the swimmer arrives at a point 40m downstream from the point directly across the river. This means that the swimmer has moved 40m in the direction of the water flow.

We also know that the river is 80m wide. This means that the distance between the starting point and the point directly across the river is 80m.

Now, let's tackle the questions:

A) What is the speed of the river current?

To answer this question, we need to use the concept of relative velocity. The speed of the river current is the speed at which the water is flowing. We know that the swimmer is moving at a speed of 1.6m/s relative to the water. Since the swimmer has moved 40m downstream, this means that the river current must be flowing at a speed of 40m/1.6s = 25m/s.

B) What is the swimmer's speed relative to the shore?

To answer this question, we need to use the concept of relative velocity again. The swimmer's speed relative to the shore is the speed at which the swimmer is moving with respect to the shore. Since the swimmer is moving at a speed of 1.6m/s relative to the water, and the river current is flowing at a speed of 25m/s, the swimmer's speed relative to the shore is the vector sum of these two velocities. This can be calculated using the Pythagorean theorem: √(1.6^2 + 25^2) = 25.2m/s. So, the swimmer's speed relative to the shore is 25.2m/s.

C) In what direction should the swimmer head in order to arrive at the point directly opposite her starting point?

To answer this question, we need to consider the direction of the swimmer's velocity. We know that the swimmer is moving at a speed