A ball is bouncing down a flight of stairs. The coefficient of...

A ball is bouncing down a flight of stairs. The coefficient of restitution is

e

. The height of each step is

d

and the ball descends one step each bounce. After each bounce it rebounds to a height

h

above the next lower step. The height is large enough compared with the width of step so that the impacts are effectively head-on. Find the relationship between

h

and

d

Options

A $h=\frac{d}{1-e^2}$
B $h=\frac{d}{1+e^2}$
C $h=\frac{d}{1+e}$
D $h=\sqrt{\frac{d}{1-e^2}}$

Correct answer

A. $h=\frac{d}{1-e^2}$

Step-by-step solution

The ball falls a distance

h

from its highest (rest) position and rebounds a distance

(h-d)

. Thus the coefficient of restitution

e=\sqrt{\frac{h-d}{h}}

e^2=\frac{h-d}{h} \quad

\quad h=\frac{d}{1-e^2}

Practice Center of Mass, Momentum and Collision on Quantrex Academy →

More from Center of Mass, Momentum and Collision

A frictionless circular wire of unit radius is fixed on the horizontal plane. Two point… NEET 2026 Bob B of mass m at rest is hanging vertically from the ceiling via a massless string of… NEET 2026 A ball of mass 0.5 kg is dropped from a height of 40 m . The ball hits the ground and… NEET 2025 Two bodies A and B of same mass undergo completely inelastic one dimensional collision.… NEET 2024 Two particles A and B initially at rest, move towards each other under mutual force of… NEET 2023 A 1 ~kg object strikes a wall with velocity 1 ~ms^ -1 at an angle of 60^ ∘ with the wall… NEET 2023 A bullet of mass m hits a block of mass M elastically. The transfer of energy is the… NEET 2023 A shell of mass m is at rest initially. It explodes into three fragments having mass in… NEET 2022 Full Center of Mass, Momentum and Collision list All NEET PYQs