River vector problem
John is on the west bank of a river that flows from north to south at a speed of $5 \text{m/s}$. She is easily able to swim at a constant speed of $1\text{m/s}$. The river is $30 \text{m}$ wide.
On what bearing should John swim to end up on the east bank at a point directly opposite her starting position?
I have spent a lot of time on this question but have not managed to prove the answer, which according to the textbook is $\text{N}~ 60^{\circ} ~\text{E}$. I have tried using vectors for the velocities to find the angle but this did not work. Any help or insight would be greatly appreciated. Thanks.
As has been pointed out by @Daniel D, it is impossible for the swimmer to swim straight across since their swimming speed is less than the speed of the river.
This is because the velocity of the swimmer relative to the water (which has magnitude $1$) is the hypotenuse of a right-angled triangle, the other sides of which are the velocity of the swimmer (relative to the bank, and going due East) and the velocity of the river (of magnitude $5$ and going due South).
The textbook must be wrong, because if the swimmer swims in the direction they say, the swimmer will end up on the opposite bank at a distance $90\sqrt{3}$ downstream from the point opposite their original position.