Understanding the Concepts
* Free Fall: An object in free fall experiences constant acceleration due to gravity (approximately 9.8 m/s²).
* Kinematics Equations: We can use the following kinematics equation to relate the initial velocity (vi), final velocity (vf), acceleration (a), and displacement (Δy) of an object in free fall:
vf² = vi² + 2aΔy
Solving the Problem
1. Identify the knowns:
* Δy = -4.85 m (negative because the displacement is downwards)
* a = -9.8 m/s² (negative because gravity acts downwards)
* vi = 0 m/s (the book is dropped, meaning it starts from rest)
2. Plug the values into the kinematics equation:
* vf² = 0² + 2(-9.8 m/s²)(-4.85 m)
* vf² = 95.06 m²/s²
3. Solve for vf (the final velocity):
* vf = √(95.06 m²/s²)
* vf ≈ 9.75 m/s
Answer: The book will have a speed of approximately 9.75 m/s just before it hits the ground.
