Question

A ball falls on an inclined plane of inclination θ from a height h above the point of impact and makes a perfectly elastic collision. Where will it hit the plane again?

Answer 1

Thanks for asking the question!

ANSWER::

Angle inclination of plane = Ф

M body falls from a height h,

Striking velocity of projectile with inclined plane, v = √2gh

Projectile makes angle (90° - 2Ф)

Velocity of projection = u = √2gh

Let AB = L

x = L cos Ф

y = - L sin Ф

From equation of trajectory ,

y = x tan α - (gx² sec²α) / 2u²

- L sinФ = L cosФ . tan (90° - 2Ф) - [g x L² cos²Ф sec²(90° - 2Ф)] / 2 x 2gh

- L sinФ = L cosФ . cot 2Ф - [gL² cos²Ф cosec² 2Ф] / 4gh

L cos²Ф cosec²2Ф / 4h = sinФ + cosФ cot 2Ф

L = 4h (sinФ + cosФ cot 2Ф) / cos²Ф cosec²2Ф

L = [ 4h x sin²2Ф (sinФ + cosФ x (cos2Ф) / (sin2Ф) ] / cos²Ф

L = 4h x 4 sin²Ф cos²Ф (sinФ x sin 2Ф + cos Ф cos 2Ф) / cos²Ф sin2Ф

L = ( 16 h sin²Ф x cos Ф ) / 2 sinФ cosФ

L = 8h sin Ф

Hope it helps!

Answer 2

very good question this question has ate my mind.