Glossary
Acceleration (multi-dimensional)
A vector quantity in multi-dimensional motion representing the rate of change of velocity, which can vary in magnitude and direction across different dimensions.
Example:
A car turning a corner while speeding up experiences acceleration that has both a tangential component (changing speed) and a centripetal component (changing direction).
Component analysis
A method used to simplify multi-dimensional motion by breaking down vectors (like velocity or acceleration) into their perpendicular x, y, and z components.
Example:
To analyze a soccer ball's flight, we use component analysis to separate its initial velocity into horizontal and vertical parts.
Horizontal motion (projectile)
The component of projectile motion along the x-axis, characterized by constant velocity and zero acceleration (assuming no air resistance).
Example:
In a long jump, once the athlete leaves the ground, their horizontal motion remains constant, covering distance at a steady speed.
Independent dimensions
The principle that motion along one perpendicular axis does not affect motion along another perpendicular axis.
Example:
When a diver jumps off a board, their horizontal motion is independent of their vertical motion, meaning gravity only affects their vertical speed, not their horizontal speed, illustrating independent dimensions.
Initial velocity components
The horizontal ($v_{0x} = v_0 \cos(\theta)$) and vertical ($v_{0y} = v_0 \sin(\theta)$) parts of an object's starting velocity, resolved from its magnitude and launch angle.
Example:
To analyze a rocket's launch, engineers first break down its launch speed and angle into its initial velocity components.
Maximum height (projectile motion)
The highest vertical position reached by a projectile during its flight, where its vertical velocity momentarily becomes zero.
Example:
A high jumper aims to achieve the greatest maximum height to clear the bar.
Multi-dimensional motion
Motion that occurs in two or three spatial directions simultaneously, requiring analysis of movement along multiple axes.
Example:
A bird flying through the air exhibits multi-dimensional motion as it moves forward, upward, and potentially sideways.
Projectile motion
The motion of an object thrown or projected into the air, subject only to the acceleration of gravity (ignoring air resistance), resulting in a parabolic trajectory.
Example:
The path of a basketball shot towards the hoop is a classic example of projectile motion.
Range (projectile motion)
The total horizontal distance covered by a projectile from its launch point to where it lands at the same initial height.
Example:
A cannon firing a projectile aims to maximize its range to hit a distant target.
SUVAT equations
A set of five kinematic equations relating displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t), used to solve problems involving constant acceleration.
Example:
Using the SUVAT equations, a student can calculate how long it takes for a car to accelerate from rest to a certain speed.
Time of flight
The total duration an object remains in the air during projectile motion, from launch until it returns to its initial height or lands.
Example:
Calculating the time of flight for a golf ball helps determine how long it will be airborne before landing on the green.
Trajectory
The path followed by a projectile or any object moving through space.
Example:
The graceful arc of a diver from the springboard into the water traces a perfect trajectory.
Velocity (multi-dimensional)
A vector quantity in multi-dimensional motion that describes both the speed and direction of an object, which can change in magnitude, direction, or both.
Example:
As a roller coaster navigates a loop, its velocity constantly changes, both in how fast it's going and the direction it's moving.
Vertical motion (projectile)
The component of projectile motion along the y-axis, characterized by constant downward acceleration due to gravity (g = 9.8 m/s²).
Example:
When a ball is tossed straight up, its vertical motion is governed by gravity, causing it to slow down, stop, and then speed up downwards.