Mechanics: Solve Swimmer A and B Problem

[magicuniverse]

Homework Statement

Swimmer A swims due east at a constant speed of 3ms^-1 along a straight stretch of river with a negligible current, keeping a constant distance of 10m from its southern bank. A second swimmer B, starts swimming from the bank when A is a distance L down the river from her (i.e. L is the distance measured along the bank). Swimmer B swims with a constant speed of 2ms^-1 and at an angle of N60E, in order to intercept A.

1) What is the velocity of B as observer by A?
2) What is the distance L? And how long does B swim for?
3) If a stong current was flowing how if at all would the above results be altered?

The Attempt at a Solution

Im really stuck on this and need some help as to what and how I should be doing. Thanks

 

[rl.bhat]

When two persons are moving in the same direction, the relative velocity is the vector difference of the two velicities. Note down the point of intersection of paths of A and B. Since width of the rever and angle of swimmer B's path with respect to north, you can find the distance covered by B and time taken by B. From these values you can find the rest of the velues.

 

[magicuniverse]

Err... i still don't know how to do that. Can anyone be a little more descriptive in what I have to do? What sort of method to I use to find the relative velocity?

 

[rl.bhat]

Vrel. = sqrt( V1^2 + V2^2 -2V1V2cos60)
Position of B, opposite point of the rever and point of intersection of the paths of A and B form right angled triange. From that you can find the distance covered by B. You know the speed of B. From that find the time taken by B. Same time is taken by A to reach the point of intersection. You know the velocity A. From that find the distance covered by A.If you substact the third side of the rt. angled triange from this distance you get L. Current in the rever changes the velocities of A and B.