Question

A particle $A$ moves along the line, $y = 30 \,m$ with a constant velocity, $v$ parallel to $x$ - axis. At the moment particle $A$ passes the $y$ - axis, a particle $B$ starts from the origin with zero initial speed and a constant acceleration, $a =0.40\, m / sec ^{2}$. The angle between $a$ and $y$ - axis is $60^{\circ}$. If the particles $A$ and $B$ collide after sometimes, then the value of $| v |$ will be

• A. 2 m / s
• B. 3 m / s
• C. 4 m / s
• D. 5 m / s

Answer 1

Answer: (B)

As shown in the figure, two particles are moving with velocity $v$ and acceleration $a$.

Let the time of collision of two particles be $t$, then the equation of motion,
$s=u t+\frac{1}{2} a t^{2}$
For particle $A$,
$30 \,m =(0) t+\frac{a \cos 60^{\circ} t^{2}}{2}$
$\Rightarrow \, 30=\frac{0.4}{2} \times \frac{1}{2} \times t^{2} $
$t =\sqrt{300}$
Hence, in time $t=\sqrt{300}$, both travelled equal distance in horizontal direction, so that the collision takes place.
$\Rightarrow u t=\frac{1}{2} a \cos 30^{\circ} t^{2}$
$\left(\because 30^{\circ}=90^{\circ}-60^{\circ}\right)$
$\Rightarrow \, u=\frac{1}{2} \times 0.4 \times \frac{\sqrt{3}}{2} \times \sqrt{300}$
$ \Rightarrow \, u=3\, m / s $