A ball which is at rest, is dropped from a height h metre....

A ball which is at rest, is dropped from a height $h$ metre. As it bounces off the floor its speed is $80 \%$ of what it was just before touching the ground? The ball $\begin{array}{ll}\text { will then rise to nearly a height } & \text { [BVP Engg. 2007] }\end{array}$ (a) $0.94 \mathrm{~h}$ (b) $0.80 h$ (c) $0.75 h$ (d) $0.64 h$

A ball which is at rest, is dropped from a height $h$ metre. As it bounces off the floor its speed is $80 \%$ of what it was just before touching the ground? The ball $\begin{array}{ll}\text { will then rise to nearly a height } & \text { [BVP Engg. 2007] }\end{array}$
(a) $0.94 \mathrm{~h}$
(b) $0.80 h$
(c) $0.75 h$
(d) $0.64 h$

Key Concepts

Gravitational Potential Energy

This is the energy an object possesses because of its position in a gravitational field. When an object is dropped from a height h, its potential energy is converted into kinetic energy as it falls, which determines its speed just before reaching the ground.

Kinetic Energy and Its Relation to Height

Kinetic energy is the energy an object has due to its motion. Through conservation of energy, the kinetic energy an object has just before impact is related to the height from which it fell, and after an impact, the new kinetic energy (which is lower due to energy loss) determines the maximum height it can reach when it bounces.

Conservation of Energy

This principle asserts that energy is neither created nor destroyed, only transformed. In the context of a bouncing ball, mechanical energy is partially conserved between potential and kinetic forms, allowing us to relate the speed before impact to the height reached after the bounce, despite losses from the collision.

Coefficient of Restitution

The coefficient of restitution quantifies the efficiency of a collision by comparing the speed after an impact to the speed just before it. In bouncing ball problems, it is expressed as the ratio of bounce speed to impact speed, and it directly influences the subsequent bounce height, as the height reached is proportional to the square of this ratio.

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