Kinematics of Projectiles: Motion, Trajectory, and Formulas
Kinematics of Projectile Motion
Defining Projectiles
- Projectiles are bodies projected into the air that possess both horizontal and vertical components of motion.
- Examples include: shot put, discus, javelin, and the human body during a jump.
- Gravity determines the maximum height achieved by the projectile.
- The horizontal component determines the maximum distance (range) the projectile reaches.
- In real-world scenarios, only air and wind resistance significantly affect the projectile’s motion.
Note on Air
Read MoreEssential Physics Practicals: Methods and Analysis
1. Mass and Weight Relationship Investigation
Step-by-Step Procedure
- Attach the spring balance or Newton meter securely so it hangs vertically.
- Place the first known mass (e.g., 100 g) on the balance hook.
- Wait for the reading to stabilize and record the weight (in Newtons, N).
- Repeat steps 2–3 for several masses (e.g., 200 g, 300 g, 400 g).
- Plot a graph of weight (N) against mass (kg).
Experimental Variables
- Independent: Mass (kg)
- Dependent: Weight (N)
- Control: Location (keep experiment on Earth, constant
Essential Biomechanics Formulas and Human Motion Principles
Core Biomechanics Formulas for Human Motion Analysis
1. Kinematics (Motion Without Forces)
Kinematics describes motion without considering the forces that cause it.
Key Linear Formulas:
- Displacement (Δx):
Δx = x₂ − x₁
Example: If a sprinter moves from 2 m to 8 m → Δx = 6 m
- Velocity (v):
v = Δx / Δt
Example: 6 m in 2 s → v = 6 / 2 = 3 m/s
- Acceleration (a):
a = Δv / Δt
Example: Speed changes from 2 m/s to 6 m/s in 2 s → a = (6−2)/2 = 2 m/s²
Angular Motion Formulas:
- Angular Displacement (θ)
Physics Fundamentals: Work, Heat Transfer, and Electrical Circuit Calculations
Work, Power, and Energy Calculations
Work Done Lifting a Load
Question: How much work is done in lifting a 500 kg load to a height of 40 m?
Answer: 1.96 × 108 J
Motor Power Calculation
Question: How powerful is a motor that can lift a 1200 kg load 10 m in 20 s?
Answer: 5886 Watts
Work and Lifting Height
Question: Which of the following statements is true regarding the work associated with lifting a box to a certain height?
Answer: All of these will require the same amount of work.
Law of Conservation of
Historical Development of Planetary Motion Theories
1. Ptolemy’s Geocentric Model (2nd Century)
- Model geocentric: the Earth is at the center of the universe.
- All the planets and fixed stars move in circular orbits around the Earth.
- To explain the motion of the planets against the background of fixed stars (retrograde motion), it was necessary to introduce epicycles and deferents.
- Although mathematically complicated, the model fit well with observations and could be applied practically (navigation, predicting eclipses, etc.).
2. Copernicus and the Heliocentric
Read MoreThe Physics of Light: Reflection, Refraction, and Vision
Fundamentals of Light and Optics
Light is a form of electromagnetic radiation, composed of both electric and magnetic fields that oscillate perpendicularly to each other. It travels in straight lines and is a fundamental form of energy that can be reflected, refracted, and absorbed.
Core Properties of Light
- Light travels at an incredible speed: 299,792,458 meters per second (approximately 186,282 miles per second) in a vacuum.
- Light is a form of energy that can be reflected, refracted, and absorbed.