Two inclined planes OA and OB intersect in a horizontal plane having their inclinations `alpha and beta` with the horizontal as shown in figure. A particle is projected from P with velocity u along a direction perpendicular to plane OA. The particle strikes plane OB perpendicularly at Q.

If `alpha = 30^@ , beta = 30^@` the time of flight from P to Q is

Options

A. `u/g`
B. `((sqrt3)u)/g`
C. `((sqrt2)u)/g`
D. `(2u)/g`

Answer

B

Explanation

At Q, component parallel to OB becomes zero

`v_x = u_x + a_xt`
`0= (u cos 30^@) + (-g sin 30^@)t`
`:. t = u/g cot 30^@ = ((sqrt3)u)/g`.