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.
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?