Relative Velocity Swimmer Problem

[SHSSpartan]

Homework Statement

A swimmer maintains a speed of 0.15 m/s relative to the water when swimming directly toward the opposite shore of a straight river with a current that flows at 0.75 m/s.

(a) How far downstream is the swimmer carried in 1.5 minutes?

(b) What is the velocity of the swimmer relative to an observer on shore?

Homework Equations

I'm not sure, sorry.

The Attempt at a Solution

I know this involves relative velocity and maybe vectors, but I am unsure. Please help.

Thank you very much.

 

[SHSSpartan]

Sorry for wasting your time, I think I understand it now.

 

[ogb p]

I would approach this problem by first defining the variables and understanding the concept of relative velocity. In this case, the swimmer's speed relative to the water is given as 0.15 m/s and the current's speed is 0.75 m/s.

Next, I would use the formula v = u + w, where v is the resultant velocity, u is the initial velocity, and w is the velocity of the current. Using this formula, I can calculate the swimmer's velocity relative to the shore by subtracting the current's velocity from the swimmer's velocity relative to the water. This gives a resultant velocity of -0.6 m/s, meaning the swimmer is moving at 0.6 m/s against the current.

(a) To determine how far downstream the swimmer is carried in 1.5 minutes, I would use the formula d = vt, where d is the distance, v is the velocity, and t is the time. Plugging in the values, I get a distance of 54 meters downstream.

(b) Finally, to calculate the swimmer's velocity relative to an observer on shore, I would use the same formula v = u + w, but this time the initial velocity (u) is the swimmer's velocity relative to the shore (which we just calculated) and the velocity of the current (w) is 0.75 m/s. This gives a resultant velocity of 0.15 m/s, meaning the swimmer appears to be stationary to an observer on shore.

In summary, the swimmer is moving at 0.15 m/s relative to the water, but appears to be moving at 0.15 m/s upstream to an observer on shore due to the current's velocity. After 1.5 minutes, the swimmer will have traveled 54 meters downstream.