Home
Class 11
PHYSICS
Two inclined planes OA and OB intersect ...

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

A

`tan^(-1) [(P^(2)+PQ +Q^(2))/(PQ)]`

B

`tan^(-1)[(P^(2)+Q^(2)-PQ)/(PQ)]`

C

`tan^(-1)[(P^(2)+Q^(2))/(2PQ)]`

D

`sin^(-1)[(P^(2)+Q^(2)+PQ)/(2PQ)]`

Text Solution

Verified by Experts

The correct Answer is:
A

The equation of trajectory.
`y = x tan alpha [1-(x)/(R)]` gives
`Q = P tan theta [1-(P)/(R)]` ...(i)
and `P = Q tan theta [1-(Q)/(R)]` ......(ii)
On dividing we get, `(Q^(2))/(P^(2)) = ([1-P//R])/([1-Q//R])`
`(1)/(R) [P^(3)-Q^(3)] = P^(2)-Q^(2)`
`R = (P^(3)-Q^(3))/(P^(2)-Q^(2)) = (P+PQ +Q^(2))/(P+Q)`
Now, `(Q)/(P) = tan theta [1-(P(P+Q))/(P^(2)+PQ+Q^(2))]`
`= tan theta [(P^(2)+PQ+Q^(2)-P^(2)-PQ)/(P^(2)+PQ+Q^(2))]`
`rArr tan theta = (P^(2)+Q^(2)+PQ)/(PQ)`
`rArr theta = tan^(-1) [(P^(2)+PQ+Q^(2))/(PQ)]`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MOTION

    DC PANDEY ENGLISH|Exercise C. Medical entrances gallery|1 Videos
  • MEASUREMENT AND ERRORS

    DC PANDEY ENGLISH|Exercise Subjective|19 Videos
  • MOTION IN A PLANE

    DC PANDEY ENGLISH|Exercise (C )Medical entrances gallery|32 Videos

Similar Questions

Explore conceptually related problems

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. The path of the particle from P to Q is

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^@ and a = 4.9 m, the initial velocity of projection is

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^@ and a = 4.9 m, the initial velocity of projection is

Two inclined planes OA and OB having inclinations 30^@ and 60^@ with the horizontal respectively intersect each other at O, as shown in figure. A particle is projected from point P with velocity u=10 sqrt(3) m//s along a direction perpendicular to plane OA. If the particle strikes plane OB perpendicular at Q. Calculate. (a) time of flight, (b) velocity with which the particle strikes the plane OB, (c) height h of point P from point O, (d) distance PQ. (Take g=10m//s^(2) )

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,

Two inclined planes OA and OB having inclination (with horizontal) 30^(@) and 60^@ (with horizontal), 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 maximum height attained by the particle (from the line O)

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 The velocity with which particle strikes the plane OB,

A stone must be projected horizontally from a point P, which is h meter above the foot of a plane inclined at an angle theta with horizontal as shown in figure . Calculate the velocity v of the stone so that in may hit the incline plane perpendiculary.

An inclined plane is inclined at theta with horizontal as shown in (figure).Write a unit vector in the direction parallel (hat(a)) and perpendicular (hat(b)) to inclined plane,in standard xy coordinate system.

Figure shows that particle A is projected from point P with velocity u along the plane and simultaneously another particle B with velocity v at an angle alpha with vertical. The particles collide at point Q on the plane. Then