# Relative velocity

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1. Jun 21, 2016

### Balsam

1. The problem statement, all variables and given/known data
A person decides to swim across a river 84m wide that has a current moving with a velocity of 0.40m/s[E]. The person swims 0.70m/s[N] relative to the water. In what direction should she swim if she lands at a point directly north of her starting position?

Note: This is part d of the question- in earlier parts we solved for the velocity of the person with respect to the earth: 0.80m/s[N 30° E], time it takes to cross the river: 1.2x10^2s, how far downstream the person will land: 48m.
2. Relevant equations
v=d/t?
3. The attempt at a solution
I assumed the speed of the person will remain the same: 0.70m/s and the speed and direction of the current will remain constant. I know the person will have to swim in the western direction to so that when the stream pushes them east, they'll land north relative to the starting position. I drew a diagram of this, where the original x and y components are the same(x component is the current's velocity and direction and y component is the swimmer's velocity and direction relative to the water, but the hypotenuse of the right triangle formed by these 2 vectors can be described as having some velocity, with the direction [N θ W], θ being its angle. I tried solving for θ using the tan ratio: tan-1(0.40/0.70)=29.74°. However, the answer in the textbook is [N 35° W]. What did I do wrong?

2. Jun 21, 2016

### billy_joule

It sounds like you've drawn the swimmers vector triangle wrong. The hypotenuse is the swimmers velocity relative to the water, (in a NW direction), it's x component is equal and opposite to the waters velocity, and the Y component is of no interest to you (swimmers velocity relative to earth).

3. Jun 21, 2016

### Balsam

Shouldn't the x component be the current? And how do we solve for the angle if we don;t know the y component?

4. Jun 21, 2016

### billy_joule

No, for the swimmer to head due north their net (ie relative to earth)x velocity must be zero, so, relative to the water, the swimmers x velocity needs to cancel the waters x velocity so should be equal and opposite.
Like running on a treadmill, you must run in the opposite direction to the belt to remain stationary relative to earth.

We know two sides (opposite & hypotenuse) so can solve for theta.