Velocity always aimed at rectilinearly moving particle

[ELiT.Maxwell]

Homework Statement

2 points A and B, B moves rectilinear with uniform velocity u and velocity of A is always aimed at B with magnitude being constant=v, initially, v is perpendicular to u and separation was L, time taken for them to collide? and equation of motion of A? (in terms of x and y with origin at initial position of A would be good, y along initial AB and X perpendicular to it and +ve x in direction of u...would be better but, at this point anything would be good) ?

Homework Equations

ds/dt=v

The Attempt at a Solution

for collision, we can take relative motion by fixing a coordinate plane at A and coordinates of B=(x,y) and dx/dt=-vcosθ+u and dy/dt=-vsinθ (couldnt really do anything with dr/dt=-v+ucosθ) dividing, dy/dx=vy/(vx-u(x²+y²)^1/2) ⇒vx.dy-u(x²+y²)^1/2).dy=vy.dx
doesnt form d(y/x)
at t=0, x=0,y=L at t=T,x=0,y=0
tried same thing with origin at initial A with tanθ=L-y/ut-x and dx/dt=vcosθ and dy/dt=vsinθ and put value of θ at t=0, x=0,y=0 at t=T, x=uT,y=L

 

[DEvens]

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