Why does a swimmer take longer to complete a trip in a river with a current?

[Ab17]

Homework Statement

A river has a steady speed of 0.500 m/s. A student swims M upstream a distance of 1.00 km and swims back to the Q/C starting point. (a) If the student can swim at a speed of 1.20 m/s in still water, how long does the trip take? (b) How much time is required in still water for the same length swim? (c) Intuitively, why does the swim
take longer when there is a current?

Homework Equations

Vse = Vsr - Vre

The Attempt at a Solution

I done this problem by adding the velocity of the swimmer and current vectorialy to get the relative speed if student w.r.t to Earth then when I searced for the solution they had just added the two speed for the upward motion and subtracted them for downward motion. I am really confused i don't know what's going on

 

[rpthomps]

Break the question up in two parts. First, find the relative velocity of the swimmer with the shore going upstream and use this to find the time. Do the same again for downstream.

 

[Ab17]

Must I do it vectorially?

 

[rpthomps]

I would. It makes it easier to understand, in my opinion.

 

[Ab17]

I got 1.09 m/s relative to the earth

 

[rpthomps]

How did you get that?

 

[Ab17]

Sqrt((1.2)^2 - (0.5)^2)

 

[rpthomps]

The velocity of the river and the velocity of the swimmer are not perpendicular to one another. Upstream means that the swimmer is parallel to the river but is working against the current. Downstream means that the current is pushing the swimmer. Knowing this, what would the addition of the vectors be in both the upstream case and the downstream one?

 

[Ab17]

This is what I done

 

[Ab17]

There will be no components for the vectors that's explains why they were just adding for going upstream and subtracting for downstream

 

[rpthomps]

Right. You have the swimmer on an angle but the question just says upstream, not going to the other bank or something like that.