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=0.40m//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

Options

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

Answer

B

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+1/2 at^(2)`
For particle A,
`30m=(0)t+(a cos 60^(@)t^(2))/(2)`
`rArr 30 = (0.4)/(2)xx1/2 xx t^(2)`
`t= sqrt(300)`
Hence, in time `t=sqrt(300)`, both travelled equal distance in horizontal direction, so that the collision takes place
`rArr ut=1/2 a cos 30^(@) t^(2) ( :. 30^(@)=90^(@)-60^(@))`
`rArr u = 1/2 xx 0.4 xx (sqrt(3))/(2) xx sqrt(300)`
`rArr u = 3 m//s`
Hence, the correct option is (b).