Calculating Relative Velocities in Rivers

[shawli]

Homework Statement

A swimmer who can swim at a speed of 0.80m/s in still water heads directly across a river 86m wide. The swimmer lands at a position on the far bank 54m downstream from the starting point. Determine

a) the speed of the current

Homework Equations

Given :
speed of swimmer relative to water = 0.80 m/s

The Attempt at a Solution

I'm not really sure how to approach this, since I've been given displacements and not velocities. How do I approach a question like this?

 

[Doc Al]

Hint: How long does it take the swimmer to get across the river?

 

[Karmalo]

Here it's what I would do:

-You know the width of the river is 86m (axis x) and you know the swimmer swims at 0.8m/s so you can get the time it takes him to cross the river. (I got 107,5s)

-Knowing that it takes him that amount of time and that he covers 54m in that direction, you can get the speed of the current by dividing the space by the time. (I got 0,502 m/s).

 

[Karmalo]

Sorry Doc Al, I started to write before you posted your message and I didn't see it.

 

[shawli]

Using the resulting displacement (Pythagorean theorem, square root of (86^2+54^2)=101.5m), I can find the time it takes for the swimmer to get across the river.

t= 101.5m/ (0,8m/s) = 126.9s.

Then ...the speed of the current can be found using this time, and the horizontal displacement?
so:
v current = 54m / 126.9s
v current = 0.43 m/s?

The answer I'm given at the back of the book is 0.5 m/s ...so I'm not sure !

 

[shawli]

Ohhhhh, I'm supposed to use the vertical displacement for the swimmers pathway.

Thank you both!

 

[Karmalo]

The swimmer is always swimming perpendicular to the river shore direction.

For example let's say the shore is the "axis y".
Displacement:
-axis x: 86m
-axis y: 54m
Velocity:
-axis x: 0,8m/s
-axis y: we have to get it

That distance you calculated is the distance he travels but that isn't what they ask you for.