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Q.

Two inclined planes (I) and (II) have inclination $α$ and $β$ respectively with horizontal, (where $α + β = 90^{0}$ ) intersect each other at point O as shown in figure. A particle is projected from point A with velocity u along a direction perpendicular to plane (I). If the particle strikes plane (II) perpendicular at B, then

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a

$t i m e o f f l i g h t = \frac{u}{g s i n β}$

b

$t i m e o f f l i g h t = \frac{u}{g s i n α}$

c

Distance $O B = \frac{u^{2}}{2 g s i n β}$

d

Distance $O B = \frac{u^{2}}{2 g s i n α}$

answer is A, C.

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Detailed Solution

Solve the problem by taking OB as X-axis and OA as Y-axis
Along OB, $a = - g \sin β$
Perpendicular to OB, $a = - g \sin β$

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Two inclined planes (I) and (II) have inclination α and β respectively with horizontal, (where α+β=900) intersect each other at point O as shown in figure. A particle is projected from point A with velocity u along a direction perpendicular to plane (I). If the particle strikes plane (II) perpendicular at B, then