A body starts falling freely from height H hits an inclined plane...

A body starts falling freely from height

H

hits an inclined plane in its path at height

h

. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of

\dfrac{H}{h}

for which the body will take the maximum time to reach the ground is _____. A body starts falling freely from height H hits an inclined plane in its path at height h . As a result of this

A body starts falling freely from height H hits an inclined plane in its path at height h . As a result of this

Correct answer

Step-by-step solution

A body starts falling freely from height H hits an inclined plane in its path at height h . As a result of this

Total time of flight $= T$ can be written as,

$T = \sqrt{\dfrac{2h}{g}} + \sqrt{\dfrac{2\left(H - h\right)}{g}}$

For maximum time $= \dfrac{dT}{dh} = 0$

$⇒ \sqrt{\dfrac{2}{g}}\left(\dfrac{1}{2\sqrt{h}} - \dfrac{1}{2\sqrt{H - h}}\right) = 0$

$⇒ \sqrt{H - h} = \sqrt{h}$

$⇒ h = \dfrac{H}{2} ⇒ \dfrac{H}{h} = 2$

Practice Motion in Two Dimensions on Quantrex Academy →

More from Motion in Two Dimensions

A particle is thrown with a speed v from a point O at an angle θ with the horizontal… JEE Advanced 2026 A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is… JEE Main 2026 Two identical bodies, projected with the same speed at two different angles cover the… JEE Main 2026 If x and y coordinates of a projectile as a function of time (t) are given as 24t and… JEE Main 2026 A gun mounted on the ground fires bullets in all directions with same speed. The farthest… JEE Main 2026 Two projectiles are projected with the same initial velocities at the 15^∘ and 30^∘ with… JEE Main 2026 A boy throws a ball into air at 45^ ∘ from the horizontal to land it on a roof of a… JEE Main 2026 An object is projected with kinetic energy K from a point A at an angle 60^ ∘ with the… JEE Main 2026 Full Motion in Two Dimensions list All JEE Main PYQs