Two inclined planes OA and OB having inclination (with horizontal) `30^(@) and 60^(@)`, respectively, intersect each other at O as shown in figure. A particle is projected from point P with velocity `u = 10sqrt3 ms^(-1)` along a direction perpendicular to plane OA. If the particle strikes plane OB perpendicularly at Q, calculate

The vertical height h of P from O,

Options

A. 10m/s
B. 5m
C. 15m/s
D. 20m

Answer

b

Explanation

Now for x-axis
`v_(x)=v_(x)+a_(x)T`
`0=10sqrt(3)-gsin 60^(@)T`
Since, `s_(x)=u_(x0T+(1)/(2)a_(x)T^(2)`
`s_(x)=(10sqrt(3).T-(1)/(2)g sin 60^(@)T^(2))`
Along y-axis
`OP=(1)/(2)g cos 60^(@)T^(2)`
`(h)/(OP)=sin 30^(@)`