A particle starts from the origin of coordinates at time t = 0 and moves in the xy plane with a constant acceleration `alpha` in the y-direction. Its equation of motion is `y= betax^2`. Its velocity component in the x-direction is

Options

A. `sqrt((2b)/a)`
B. `sqrt(a/(2b))`
C. `sqrt(a/b)`
D. `sqrt(b/a)`

Answer

B

Explanation

`y = bx^(2)` ……….. (i)
Equation of projectile
`y = x tan theta - (gx^(2) (1 + tan^(2) theta))/(2u^(2))`…….. (ii)
On comparing (i) and (ii)-
`tan theta = 0 rArr theta = 0, u_(x) = u_(y)=0`
and `b =g/(2u^(2))`, here g = a
`rArr u^(2) = a/(2b) rArr u = sqrt(a/(2b))`
`therefore u_(x) = sqrt(a/(2b))`