Need help with 3d relative velocity h/w problem

[dk702]

Here the question,

A swimmer wants to cross a river, from point A to point B. The distance d_1 (from A to C) is 200 m, the distance d_2 (from C to B) is 150 m, and the speed v_r of the current in the river is 5 km/h. Suppose that the swimmer makes an angle of theta=45 deg. (0.785 radians) with respect to the line from A to C.


To swim directly from A to B, what speed v_s, relative to the water, should the swimmer have?

I think this is the eq. i need. velocity vector(swimmer with respect(wrt) to earth)= velocity vector(swimmer wrt river)+ velocity vector(river wrt earth)

my values so far, that I know are wrong

v_(s/e)=9km/hr
v_(r/e = 5km/hr
v_(s/r)= 7.5

If the swimmer wanted to swim from A to C i could solve it. It is that he wants to swim from A to B that is giving trouble.

To give you an idea of my skill level:
I can solve a problem such as this;

The compass on an airplane indicates it is heading due north and its airspeed indicator shows that it is moving through the air at 240km/h. If there is a wind of 100km/h from the west, what is the velocity of the plane relative to the earth? What direction should the pilot head to travel due north and what will be his velocity relative to the Earth then?

v_(p/e)=260km/h at 23 deg E of N

and v_(p/e) = 218km/h at 25 deg W of N

 

[HallsofIvy]

Where is C in relation to A and B??

You say that "The distance d_1 (from A to C) is 200 m, the distance d_2 (from C to B) is 150 m " but that doesn't help unless we know the angles formed. Is C on the line from A to B? That would be the easiest case: Then just ignore C and take the distance from A to B to be 350 m but surely it's not that simple.

 

[NJones]

Originally posted by HallsofIvy
Where is C in relation to A and B??

You say that "The distance d_1 (from A to C) is 200 m, the distance d_2 (from C to B) is 150 m " but that doesn't help unless we know the angles formed. Is C on the line from A to B? That would be the easiest case: Then just ignore C and take the distance from A to B to be 350 m but surely it's not that simple.

i think he could be talking of a triangle...I should know how to do this... i'll need to find my maths brain...

 

[HallsofIvy]

But none of "knows how to do it" until we know where C is!

 

[NJones]

Originally posted by HallsofIvy
But none of "knows how to do it" until we know where C is!

I was meaning if it was a triangle