What is the Correct Setup for River Relative Velocity Homework?

[Toranc3]

Homework Statement

Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 1 h, reaching a point 2 Km farther upstream. At this point they realize that the bottle is missing and, driven by ecological awareness, they turn around and head downstream. They catch up with and retrieve the bottle (which has been moving along with the current) 5 Km downstream from the turn-around point.

I am wondering if the setup in my picture is correct. I have my work on there.

Homework Equations

The Attempt at a Solution

Vc/w = velocity of the canoe relative to the water.
Vc/e= velocity of the canoe relative to the earth.
Vw/e= velocity of the water relative to the earth.

Vc/e=Vc/w + Vw/e

 

[mfb]

There is an easy way to get t2 without any calculation. This allows to get the river velocity quickly, and afterwards the problem is easy to solve.

I disagree with your equations V1=Vc/w and V2=Vc/w. The 2 and 5km refer to earth.

 

[Toranc3]

There is an easy way to get t2 without any calculation. This allows to get the river velocity quickly, and afterwards the problem is easy to solve.

I disagree with your equations V1=Vc/w and V2=Vc/w. The 2 and 5km refer to earth.

Yeah I messed up. How would you go about getting the time without calculations? By the way I got it.

 

[mfb]

Consider the problem in the frame of the bottle.

 

[Nickie]

In this problem, the students are canoeing on a river, which means that they are moving relative to the water. Therefore, the velocity of the canoe relative to the earth (Vc/e) is equal to the velocity of the canoe relative to the water (Vc/w) plus the velocity of the water relative to the earth (Vw/e). This setup is correct and can be used to solve the problem.

To solve for the velocities, we can use the given information that the students paddled for 1 hour and traveled 2 km upstream, and then traveled an additional 5 km downstream to retrieve the bottle. We can also assume that the speed of the current is constant.

Using the formula V = d/t, we can calculate the velocity of the canoe relative to the water as 2 km/h upstream and 5 km/h downstream. This means that the velocity of the canoe relative to the earth is 2 km/h slower than the velocity of the water relative to the earth (since the students are paddling against the current and with the current, respectively).

Therefore, the setup in your picture is correct and can be used to solve the problem. Just remember to use the appropriate signs (+/-) for the velocities based on the direction of travel.