Understanding the Physics
* Free Fall: The book is falling freely, meaning the only force acting on it is gravity.
* Conservation of Energy: As the book falls, its potential energy (due to its height) is converted into kinetic energy (due to its motion).
The Solution
1. Potential Energy (PE): The initial potential energy of the book is given by:
PE = mgh, where:
* m is the mass of the book
* g is the acceleration due to gravity (approximately 9.8 m/s²)
* h is the height of the desk
2. Kinetic Energy (KE): Just before hitting the floor, all the potential energy is converted into kinetic energy:
KE = 1/2 mv², where:
* m is the mass of the book
* v is the final velocity of the book
3. Equating Energies: Since energy is conserved:
PE = KE
mgh = 1/2 mv²
4. Solving for Velocity:
* Cancel out the mass (m) on both sides.
* Multiply both sides by 2: 2gh = v²
* Take the square root of both sides: √(2gh) = v
Therefore, the speed of the book upon striking the floor is:
v = √(2gh)
