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^ . If the particles A and B collide after sometimes, then the value of | v | will be

Step-by-step solution

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+ 1 2 a t^2 For particle A , aligned 30 ~m & =(0) t+ a 60^ t^2 2 30 & = 0.4 2 1 2 t^2 t & = 300 aligned Hence, in time t= 300 , both travelled equal distance in horizontal direction, so that the collision takes place. u t= 1 2 a 30^ t^2 ( 30^ =90^ -60^ ) aligned & u= 1 2 0.4 3 2 300 & u=3 ~m / s & aligned Hence, the correct option is (2).