How Does a Swimmer Navigate a River with a Current?

[tphy_08]

Homework Statement

A man can swim at 2ms^-1 ( with neglible acceleration) across a current of 1ms^-1. He swims towards a point directly opposite his starting position on the river, 10m wide, and always aims to swim across to this point wherever he is on the river

a) find how long it takes for him to swim across
b) sketch the curve the man would swim across the river.
c) find the equation of the curve he swims, assuming the start point is the origin

http://img512.imageshack.us/img512/6983/hardsuvattz4.jpg

Homework Equations

Any calculus equations
Any SUVAT or motion equations

The Attempt at a Solution

I don't really know where to start at all with this question because its for extra credit but any help, guidance or worked through answers would be great =)

 

[Hootenanny]

Homework Statement

A man can swim at 2ms^-1 ( with neglible acceleration) across a current of 1ms^-1. He swims towards a point directly opposite his starting position on the river, 10m wide, and always aims to swim across to this point wherever he is on the river

a) find how long it takes for him to swim across
b) sketch the curve the man would swim across the river.
c) find the equation of the curve he swims, assuming the start point is the origin

Homework Equations

Any calculus equations
Any SUVAT or motion equations

The Attempt at a Solution

I don't really know where to start at all with this question because its for extra credit but any help, guidance or worked through answers would be great =)

Welcome to Physics Forums.

We don't provide worked solutions, but we will help you through the problem. The first point to realize is that motion in perpendicular directions is independent. In other words, we can just look at the component of the swimmers velocity going across the river, and ignore the component of his velocity direction down the river, and vice versa.

Knowing this and considering the component of velocity going across the river, can you determine the time taken for the swimmer to cross the river?

 

[tphy_08]

So therefore the swimmer would take 5s to cross the river, if there was no current. But his speed would be affected by the fact he is not always swimming directly across, but also slightly upstream at an angle as he starts swimming. how would i compensate for this in my calculation?
Thanks

 

[Hootenanny]

So therefore the swimmer would take 5s to cross the river, if there was no current. But his speed would be affected by the fact he is not always swimming directly across, but also slightly upstream at an angle as he starts swimming. how would i compensate for this in my calculation?
Thanks

Five seconds is the correct answer. Reread my first paragraph in the post above, its an extremely important point to realize in kinematics. That is that motion in perpendicular directions is independent. You are indeed correct that his speed (and velocity) will be affected by the current, however the horizontal component will not. In other words, he will still be swimming across the river at 2m/s, but he will also be traveling down the river at 1m/s.

Do you follow?