I've been having trouble with this relative motion physics problem. Could someone help me?

Question

A swimmer wants to cross a river, from point A to point B. The distance d1 (from A to C) is 200 m, the distance d2 (from C to B) is 150 m, and the speed vr of the current of the river is 5 km/hour. Suppose that the swimmer makes an angle of theta = 45 degrees (0.785 radians) with respect to the line from A to C. To swim directly from A to B, what speed is vs, relative to the water, should the swimmer have?

There's a figure attached, so I'll kind of explain it a little. If the line from A to C is the positive y direction, the line C to B is in the +y direction. The river current is 5 km/hour in the +x direction, while the swimmer has an angle of theta going in the -x and -y direction, so the swimmer is swimming in a kind of opposite direction from where the swimmer really wants to be.

Thanks so much for any help!

Sorry! d2 from C to B is going in the +x direction.

C B
------------
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|
S | ----> River at 5 km/hr
\ |
\ |
A

Here's a rough sketch of the diagram, haha. The \'s is the velocity vectory of the swimmer, and there's a 45 degree angle between the swimmer and the line from A to C. The swimmer wants to go from A to B.

haha, that didn't work....but thanks for all the help anyway, sorry for the confusion

Answer 1

The fundamental concept involved here is that velocity is a vector. So if someone is moving at an angle to the current then his velocity can be split into components which are horizontal and vertical(in the direction or opposite) to the current. I couldn't really make out the diagram you are trying to show so I will give a general solution.
If the river is flowing towards -ve x axis with velocity v and a person is trying to cross the river at an angle a(to positive x axis) against the flow with a velocity u.
Then persons velocity can be split into
u cos a, in x direction and u sin a in y direction
So the relative velocity is
v - u cos a in the x direction and u sin a in the y direction.
This means the person will take d/(u sin a) time to cross the river where d is the distance between the banks.
The person would have moved a distance (v - u cos a)*d/(u sin a)
in the x direction while crossing the river.

Hope this helps!

Answer 2

The question, as stated, has a mistake and can't be solved. Both the AC and CB lines can not be going in the +y direction as stated. A better description would help. I assume that one of these lines goes straight across the river, so a right angle is involved and can be used for solving the 3rd side. Then the swimmer is going cross, losing speed to the current to make the crossing at an angle (other than 45 which is the swimming angle) to one of the lines. But not from this description.

Answer 3

you're heading in the right route. the area must be a similar, so if v(b) is the fee of the boat relative to the river and v(r) is the fee of the river, then {v(b) + v(r)} t(a million) = {v(b) - v(r)} t(2) although the left bracket is purely 10 km/h and the right bracket is 6 km/h. From those expressions you'll get the fee of the river (and also the boat).