Grade 10
  1. Mechanics  1.1. Dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration  1.1.6. Graphical representation of motion  1.1.7. Equations of motion  1.1.8. Free fall and acceleration due to gravity  1.1.9. Projectile motion  1.1.10. Relative speed  1.2. Dynamics  1.2.1. Newton's Laws of Motion  1.2.2. Inertia and mass  1.2.3. Force and its types  1.2.4. action and reaction force  1.2.5. Friction and its effects  1.2.6. Coefficient of friction  1.2.7. Circular motion  1.2.8. Centripetal force and centripetal acceleration  1.2.9. Momentum and Impulse  1.2.10. Conservation of momentum  1.2.11. Newton's third law and applications  1.3. Work, Energy and Power  1.3.1. Work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy  1.3.5. Mechanical energy  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.3.8. Renewable and non-renewable energy sources  1.4. Gravitational force  1.4.1. Newton's law of universal gravitation  1.4.2. Gravitational field and field strength  1.4.3. Acceleration due to gravity on different planets  1.4.4. Kepler's laws of planetary motion  1.4.5. Orbits and satellites  1.4.6. Weight and apparent weight  1.4.7. Gravitational potential energy
  2. Properties of matter  2.1. States of matter  2.1.1. Solid, liquid and gas  2.1.2. Molecular structure of matter  2.1.3. Intermolecular forces  2.1.4. Plasma and Bose–Einstein condensate  2.2. Pressure  2.2.1. Definition of Pressure  2.2.2. Pressure in liquids  2.2.3. Atmospheric pressure  2.2.4. Pascal's principle  2.2.5. Archimedes' Principle and Buoyancy  2.2.6. Surface tension and capillarity  2.3. Elasticity  2.3.1. Hooke's law  2.3.2. Stress and strain  2.3.3. Elastic Limit and Modulus of Elasticity  2.3.4. Applications of Elasticity
  3. Thermal physics  3.1. heat and temperature  3.1.1. Difference Between Heat and Temperature  3.1.2. Temperature scale  3.1.3. Thermal expansion  3.1.4. Thermal equilibrium  3.2. Heat transfer  3.2.1. Conductivity  3.2.2. Convection  3.2.3. Radiation  3.2.4. Insulation and its applications  3.3. Thermal properties of matter  3.3.1. Specific heat capacity  3.3.2. Latent heat and phase change  3.3.3. Boiling and Melting Point  3.3.4. Heat engines and refrigeration  3.4. Laws of Thermodynamics  3.4.1. Zeroth law of thermodynamics  3.4.2. First law of thermodynamics  3.4.3. Second law of thermodynamics  3.4.4. Carnot cycle
  4. Waves and optics  4.1. Nature and properties of waves  4.1.1. Types of waves in nature and properties of waves  4.1.2. Transverse and longitudinal waves  4.1.3. Wave parameters  4.1.4. Reflection and refraction of waves  4.1.5. Superposition and Interference  4.1.6. Standing Waves and Resonance  4.1.7. Doppler effect  4.2. Sound waves  4.2.1. Characteristics of sound waves  4.2.2. Speed of sound in different mediums  4.2.3. Applications of sound waves  4.2.4. Ultrasound and its uses  4.3. Light Waves and Optics  4.3.1. Nature of light  4.3.2. Reflection of light  4.3.3. Laws of reflection  4.3.4. Mirrors and Image Formation  4.3.5. Refraction of light  4.3.6. Snell's Law  4.3.7. Lenses and Image Formation  4.3.8. Total internal reflection and critical angle  4.3.9. Optical fibre  4.4. Optical Instruments  4.4.1. Microscope  4.4.2. Telescope  4.4.3. Human eye and vision defects  4.4.4. Camera and its working principle
  5. Electricity and Magnetism  5.1. Electrostatics  5.1.1. Electric charge and its properties  5.1.2. Conductors and Insulators  5.1.3. Coulomb's law  5.1.4. Electric field and field lines  5.1.5. Electric potential and potential difference  5.1.6. Capacitors and Capacitance  5.2. Current Electricity  5.2.1. Electric current and its measurement  5.2.2. Ohm's law  5.2.3. Resistance and resistivity  5.2.4. Series and Parallel Circuits  5.2.5. Electric power and energy  5.2.6. Kirchhoff's Laws  5.3. Magnetism and Electromagnetism  5.3.1. Magnetic field and field lines  5.3.2. Magnetic effects of electric current  5.3.3. Electromagnetic induction  5.3.4. Faraday's laws of electromagnetic induction  5.3.5. Transformers and Applications  5.3.6. AC and DC current
  6. Modern Physics  6.1. Nuclear physics  6.1.1. Structure of the atom  6.1.2. Bohr's atomic model  6.1.3. Electron Energy Levels  6.1.4. X-rays and applications  6.2. Radioactivity  6.2.1. Types of radiation  6.2.2. Half-life and radioactive decay  6.2.3. Nuclear reactions and applications  6.2.4. Fission and Fusion  6.3. Quantum physics  6.3.1. Wave–particle duality  6.3.2. Photoelectric effect  6.3.3. Energy quantization  6.3.4. Heisenberg's uncertainty principle
  7. Electronics and Communication  7.1. Semiconductors  7.1.1. Conductors, Insulators and Semiconductors  7.1.2. Diodes and their applications  7.1.3. Transistors and Logic Gates  7.1.4. LEDs and photodiodes  7.2. Communication Systems  7.2.1. Basics of communication  7.2.2. Analog and digital signals  7.2.3. Wireless and optical fibre communication  7.2.4. Radio Waves and Modulation

Grade 10 → Mechanics → Dynamics ↓


Projectile motion


Projectile motion is a type of motion experienced by an object or particle that is thrown near the Earth's surface and moves along a curved path under the action of gravity only (assuming air resistance is negligible). The path that the object follows is called its trajectory. Projectile motion is an important concept in physics because it shows how motion works in two dimensions when gravity is the only force acting on the object.

Understanding projectile motion

To understand projectile motion, we need to break it down into two components: horizontal and vertical motion. These motions are independent of each other but happen simultaneously.

Example: throwing a ball

When you throw a ball, the ball moves in both vertical and horizontal directions at the same time. Its behavior in each of these directions can be studied separately:

  • Horizontal motion: In the absence of air resistance, the horizontal component of the velocity of a projectile remains constant. This is because gravity does not affect horizontal motion.
  • Vertical motion: Vertical motion is affected by gravity, which accelerates the object downward at a speed of 9.81 m/s2. This causes the vertical component of the projectile's velocity to vary with time.

Equations of projectile motion

The motion of a projectile is expressed mathematically using the equations of dynamics. Here are the primary equations used to calculate various aspects of the motion of a projectile:

Horizontal speed

x = v x t

Where:

  • x is the horizontal displacement.
  • v x is the horizontal velocity, which is constant.
  • t is the time of flight.

Vertical speed

y = v y0 t - 0.5gt 2

Where:

  • y is the vertical displacement.
  • v y0 is the initial vertical velocity.
  • g is the acceleration due to gravity (9.81 m/s2).
  • t is the time of flight.

Key features of projectile motion

Several key features of motion can be observed in projectile motion:

  • Parabolic trajectory: The shape of the path followed by a projectile is a parabola. This is due to the combination of constant horizontal motion and accelerated vertical motion.
  • Maximum altitude: The highest point of the trajectory, where the vertical component of velocity is zero.
  • Range: The horizontal distance traveled by a projectile from the point of launch to the point where it strikes the ground.
  • Symmetry: The trajectory of a projectile is symmetrical. It takes the same time to reach the maximum height as it takes to fall back to the same level.

Demonstration with examples

Example calculation

Suppose you are standing on a hill and throw a ball at an angle of 30° to the horizontal with an initial velocity of 20 m/s.

Step 1: Calculate the initial velocity components

First, split the initial velocity into horizontal and vertical components:

v x = v 0 * cos(θ) v y0 = v 0 * sin(θ)

where v 0 is the initial velocity and θ is the angle of projection.

For our example:

v 0 = 20 m/s; θ = 30° v x = 20 * cos(30°) = 20 * (√3/2) ≈ 17.32 m/s
v y0 = 20 * sin(30°) = 20 * (1/2) = 10 m/s

Visual representation of projectile motion

Projection Point Landing Point Maximum height

Step 2: Calculate the flight time

To find the time the ball is in the air, use the vertical motion equation. The time to reach the maximum height is the same as the time to fall back down, if the starting and final heights are equal:

t = (2 * v y0 ) / g

So for our example:

t = (2 * 10) / 9.81 ≈ 2.04 seconds

Step 3: Calculate the range

The range is the horizontal distance covered:

Range = v x * t

And for our example:

Range = 17.32 * 2.04 ≈ 35.34 meters

Step 4: Calculate the maximum height

Use the vertical speed formula to find the maximum height:

H = (v y0 2 ) / (2 * g)

And for our example:

H = (10 2 ) / (2 * 9.81) ≈ 5.10 meters

Importance of projectile motion in real life

Understanding projectile motion is important not only in theoretical physics but also in practical applications. Here are some real-world applications:

  • Sports: Sports such as basketball, soccer, and javelin throw involve understanding projectile motion to calculate flight distance, time, and proper techniques.
  • Engineering: Engineers use the concepts of projectile motion when designing trajectories for various machines and devices, such as in ballistics and space missions.
  • Animation and video gaming: Experts use projective motion principles to simulate realistic movements of characters and objects.
  • Archaeology and history: Understanding ancient weapons, such as how catapults worked, requires a detailed knowledge of projectile motion.

Dealing with common misconceptions

Some misconceptions students may have about projectile motion are:

  • Horizontal and vertical motion affect each other: In reality, this does not happen. These motions are independent, and the horizontal velocity does not affect the vertical motion and vice versa.
  • Change in horizontal velocity: Students often think that the horizontal component of velocity changes like the vertical component. It remains constant in the absence of air resistance.

In projectile motion, looking at two components separately and knowing their contribution to the overall path is an essential skill for students.


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Projectile motion

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