What is Motion under Gravity?
Motion under gravity refers to the movement of ob

What is Motion under Gravity?
Motion under gravity refers to the movement of objects under the influence of gravity, which is the force of attraction between masses. On Earth, gravity pulls objects towards its center, resulting in a downward acceleration.
Key Concepts:
1. Free Fall: An object falls towards the ground with a constant acceleration (g = 9.8 m/s²).
2. Gravity: Force of attraction between masses, directed towards the center of the Earth.
3. Acceleration due to Gravity (g): 9.8 m/s² (on Earth’s surface).
4. Velocity and Displacement: Increase linearly with time under constant acceleration.
5. Projectile Motion: Motion under gravity, with horizontal and vertical components.
Equations:
1. Velocity-time: v = u + gt
– v: final velocity
– u: initial velocity
– g: acceleration due to gravity
– t: time
2. Displacement-time: s = ut + (1/2)gt²
– s: displacement
– u: initial velocity
– g: acceleration due to gravity
– t: time
3. Velocity-displacement: v² = u² + 2gs
– v: final velocity
– u: initial velocity
– g: acceleration due to gravity
– s: displacement
Types of Motion:
1. Free Fall: Object falls vertically under gravity.
2. Projectile Motion: Object moves horizontally and vertically under gravity.
3. Motion on an Inclined Plane: Object moves along a sloping surface under gravity.
Important Points:
1. Acceleration due to gravity is constant (9.8 m/s²).
2. Velocity and displacement increase linearly with time.
3. Projectile motion has both horizontal and vertical components.
4. Range and maximum height depend on initial velocity and angle of projection.
Formulas
1. Time of flight (T): T = 2u sin(θ) / g
2. Range (R): R = u² sin(2θ) / g
3. Maximum height (H): H = u² sin²(θ) / (2g)
Graphs:
1. Velocity-time graph: Linear increase
2. Displacement-time graph: Parabolic increase
3. Velocity-displacement graph: Parabolic increase
Applications:
1. Projectile motion in sports (e.g., golf, basketball)
2. Space exploration (e.g., satellite orbits)
3. Construction and engineering (e.g., building design)
Common Mistakes:
1. Forgetting to include gravity’s effect on motion
2. Confusing velocity and acceleration
3. Incorrectly applying formulas and equations
Tips for Problem-Solving:
1. Break down complex problems into simpler components
2. Identify the type of motion (free fall, projectile, etc.)
3. Use relevant equations and formulas
Example Problems:
1. An object is dropped from rest at a height of 20 m. Find its velocity and displacement after
2 seconds.
2. A ball is thrown horizontally from a height of 10 m. Find its range and maximum height.
3. A car accelerates down an inclined plane. Find its velocity and displacement after 5 seconds.