Intercepting Vectors: Calculating Rower A's Path to Catch a Floating Object

[ally79]

Homework Statement

Rower A is stationary at the point A adjacent to the river bank when he spots an object floating down the river. He estimates that the object is 50m away and heading south at a speed of 3m/s (the same speed as the current) see diagram below.

Assuming rower A can sustain a rowing speed of 4m/s

1 Draw a diagram of the velocity vectors involved if rower a is to intercept the object

2 calcuate the direction with respect to the river bank he needs to row (in degrees) in order to achieve his goal.

Homework Equations

The Attempt at a Solution

I'm lost at where to begin with this question I can work out the initial horizontal distance and the initial vertical distance. I know that the vertical displacement of the rower plus the vertical displacement of the object must equal the initial vertical distance. After that I'm stumped. Any help with this is apprecciated

 

[Dick]

Pick a coordinate system, say with (0,0) at A and call t=0 when the rower starts. You know the object is moving with the current (velocity (0,-3)) and starts at B. Can you write an equation for the position of the object at any time? Now pick and angle for the rower to start say 'a'. Then the velocity of the rower is (v*cos(a),v*sin(a))+(0,-3) since he's dragged by the current. Can you write an equation for the position of A at any time t? Now equate x and y. That gives you two equation in the two unknowns t and a. Can you solve them?