Question

A moves with constant velocity u along then x-axis. B always has velocity towards A. After how much time will B meet A if B moves with constant speed V? What distance will be travelled by A and B?

Answer 1

Let at any instant the velocity of B makes an angle $\alpha$ with that of x-axis and the time to collide is T.
$V_{app}=V-ucos\alpha$
$l={\int }_0^T{V}_{app}dt$
$={\int }_0^T(V-ucos\alpha )dt$ ...(i)
Now equating the displacement of A and B along x direction, we get
$uT=\int Vcos\alpha dt$
Now from (i) and (ii), we get
$l=VT-{\int }_0^{T}ucos\alpha dt$
$=VT-\frac{u}{V}{\int }_0^{T}Vcos\alpha dt=VT-\frac{v}{V}.uT$
$\Rightarrow T=\frac{lV}{v^2-u^2}$
Now distance travelled by A and B
$=u\times \frac{lV}{v^2-u^2}$ and $v\times \frac{lV}{v^2-u^2}$
$=\frac{uVl}{V^2-u^2}$ and $\frac{V^{2}l}{V^2-u^2}$