Question

A particle $A$ moves along the line, $y=30m$ 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, $a=0.40m/se{c}^2$. 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,
$s=ut+\frac{1}{2}a{t}^2$
For particle $A$,
$30m=(0)t+\frac{a\cos 60^{\circ }{t}^2}{2}$
$\Rightarrow 30=\frac{0.4}{2}\times \frac{1}{2}\times t^2$
$t=\sqrt{300}$
Hence, in time $t=\sqrt{300}$, both travelled equal distance in horizontal direction, so that the collision takes place.
$\Rightarrow ut=\frac{1}{2}a\cos 30^{\circ }{t}^2$
$\left(\because 30^{\circ }=90^{\circ }-60^{\circ }\right)$
$\Rightarrow u=\frac{1}{2}\times 0.4\times \frac{\sqrt{3}}{2}\times \sqrt{300}$
$\Rightarrow u=3m/s$