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Two inclined planes OA and OB having inc...

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 = 10(sqrt3) ms^(-1)` along a direction perpendicular to plane OA. If the particle strikes plane OB perpendicularly at Q, calculate

Time of flight of the particles

Text Solution

Verified by Experts

Let us choose the x and y directions along OB and OA respectively. Then, `u_x=u=10sqrt3m//s,u_y=0`
`a_x=-gsin60^(@)=-5sqrt3m//s^2`
and `a_y=-g cos 60^(@)=-5m//s^(2)`
At point Q, x-component of velocity is zero
Hence, substituting in
`v_x=u_x+a_xt`
`0=10sqrt3-5sqrt3timpliest(10sqrt3)/(5sqrt3)=2s`
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