Motion Under Gravity in 2 Dimensions

Understanding Motion Under Gravity in 2 Dimensions

• Two-dimensional motion under gravity refers to the movement of an object under the influence of gravitational force (typically downwards) while also having a horizontal component of motion.
• Such motion can display a parabolic path, especially in the absence of air resistance.
• The effects of gravity are only felt in the vertical component of motion. The horizontal component remains constant if air resistance is ignored.

Key Concepts and Principles

• Gravity is the vertical force acting on an object in motion. The acceleration due to gravity is usually represented as ‘g’.
• The vertical component of such motion can be treated as a special case of uniformly accelerated motion where the acceleration is equal to ‘g’.
• The horizontal motion can be considered as uniform motion as it remains unaffected by gravity (in the absence of air resistance).

The Equations of Motion

• The equations of motion can be used to describe the object’s behaviour under gravity. These equations include:
  • Final velocity, v = u + gt
  • Vertical displacement, s = ut + 0.5gt²
  • Velocity squared, v² = u² + 2gs
• It’s crucial to remember that the initial vertical velocity (‘u’) is zero if the object starts from rest.

Solving Problems Involving Motion Under Gravity in 2 Dimensions

• For effective problem-solving, break down the motion into two independent components - horizontal and vertical.
• Free body diagrams can visualise the forces acting on an object in such scenarios, aiding understanding and calculation.
• When encountering problems, use the principles of vector resolution, vector addition, and other related concepts to dissect and solve the problem effectively.

Effects of Air Resistance

• While ideal questions often ignore air resistance, it is worth noting that air resistance plays a crucial role in real-world scenarios.
• Air resistance can significantly alter the trajectory, maximum height and time of flight of a projectile.
• It adds a vertical retardation force, and a horizontal force that gradually slows down the horizontal component of motion.
• Understanding how to factor this in when required can enhance problem-solving capabilities.

Further Consideration: Angled projections

• In addition to vertical drops and horizontal throws, projectiles can also be launched at an angle. Here, both the horizontal and vertical components of initial velocity need to be considered.
• Initial velocity, launch angle, and height of release becomes critical factors determining the trajectory, range, and time of flight.
• Mastery in trigonometric principles is necessary to decompose and analyse the launch velocity in such scenarios.

Remember to refer frequently back to the fundamental laws of physics and principles of mechanics when studying two-dimensional motion under gravity. Whether it’s the constancy of horizontal velocity or the acceleration due to gravity impacting vertical motion - a firm grasp of these principles is the key to successfully mastering this topic.