A particle moves along a straight line parallel to x-axis at a distancce `d = 3`m from it, with constant speed of `v = 3 m//s`. Another particle stats from the origin with constant acceleration `a = 4 m//s^(2)` at an angle `theta` with y-axis along a straight line at the instant the first particle crosses y-axis. Find 'theta' such that the two particle collide.

Options

A. `0^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Answer

D

Explanation

At the time of collision (x, y) coordinate of both the particle will be equal hence,
`X_(1) = vt`
`Y_(1) = d`
`X_(2) = (1)/(2)` a `(sin theta).t^(2)`
`Y_(2) = (1)/(2) " a " (cos theta).t^(2)`
`vt = (1)/(2) (" a " sin theta).t^(2)`
`d = (1)/(2) " a " (cos theta).t^(2)`
solving equations, we get
`t = (2v)/(a sin theta)`
`theta = 60^(@)`