Question

Particle A moves uniformly with velocity v, so that vector v is continually aimed at point B which moves rectilinearly with a velocity u < v. At t = 0, v and u are perpendicular. Find the time when they converge. Assume A and B are separated by $l$ at t = 0.

• A. $\frac{lu}{(v^2-u^2)}$
• B. $\frac{lv}{(v^2-u^2)}$
• C. $\frac{l}{u}$
• D. $\frac{l}{v}$

Answer 1

The correct option is B $\frac{lv}{(v^2-u^2)}$

A approaches B with a velocity = v - u cos $\alpha$
$\frac{dx}{dt}=v-ucos\alpha$
$\Rightarrow {\int }_0^{l}dx={\int }_0^t(v-ucos\alpha )dt$
$\Rightarrow \frac{l-vt}{u}=\int -cos\alpha dt\left(1\right)$
From the given figure: ut = $\int vcos\alpha dt\left(2\right)$
From Eqs. (1) and (2)
$ut=\frac{-v(l-vt)}{u}$
$\Rightarrow u^{2}t=-vl+v^{2}t$
$\therefore t=\frac{lv}{(v^2-u^2)}$
Hence, the correct answer is option (b).