Discussion Forum

A particle A moves along the line, y=30m with a constant velocity, v parallel to the x-axis. At the momemt particle A passes the y-axis, particle  B starts from the origin  witrh zero  initial speed and a constant acceleration  .$a=0.40 m/sec^{2}$ . The angle between a and y-axis is $60^{0}$. If the particles A and B collide after sometimes , then the value of |v|  will be

Answer:

Explanation:

 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

 $s=ut+\frac{1}{2} at^{2}$

 For particle A,

     $0m =(0) t +\frac{a \cos 60^{0} t^{2}}{2}$

 $\Rightarrow$         $30= \frac{0.4}{2} \times \frac{1}{2} \times t^{2}$

   $t= \sqrt {300}$

 Gence, in time t = $\sqrt{300}$  , both travelled equal distance in horizontal direction , so that the collision takes place.

 $\Rightarrow$     $ut=\frac{1}{2}  a \cos 30^{0} t^{2}( \because  30^{0}=90^{0}-60^{0}$)

  $\Rightarrow$     $u= \frac{1}{2}\times 0.4 \times\frac{\sqrt{3}}{2}\times\sqrt{300}$

 $\Rightarrow$      u=3 m/s

 Hence , the correct option is (b)