Mechanics: Projectile Motion

Key Concepts

Projectile motion refers to the motion of an object thrown or projected into the air, subject only to the force of gravity and air resistance.
Gravity is the only significant force acting upon a projectile in flight. The force of air resistance is negligible for objects studied in A level physics.
The motion of a projectile can be analysed as two independent motions: a vertical motion under constant acceleration due to gravity, and a horizontal motion with constant velocity. These two motions occur simultaneously.
Independence of motions: The vertical motion and horizontal motion are independent of each other. This means that any change in an object’s horizontal speed will not affect its vertical speed, and vice versa.
Trajectory of a projectile: A projectile follows a curved path known as a parabola, regardless of the angle at which it is launched.

The vertical motion is a uniformly accelerated motion, often described by the equation s = ut + 0.5at², where s is the displacement, u is the initial vertical velocity, t is the time, and a is the constant acceleration due to gravity (about -9.8 m/s²).
The horizontal motion is a uniform motion and can be described by the equation s = vt, where s is the displacement, v is the constant horizontal velocity, and t is the time.

Range (horizontal distance) and maximum height can be calculated using the equations of motion and trigonometry.
If an object is launched with an initial velocity of u at an angle θ, the initial vertical velocity (u sin θ) and initial horizontal velocity (u cos θ) can be found.
The time of flight (2u sin θ/g) and maximum height reached (u² sin² θ/2g) can also be calculated.

Projectile motion is prevalent in sports such as football, cricket and athletics, where understanding the parabolic trajectory can help enhance performance.
Understanding projectile motion also has applications in areas like military strategy, physics-based games, and space exploration, where predicting and controlling the trajectory of objects is crucial.

When dealing with projectile motion, the motion in the vertical direction is a uniformly accelerated motion, while the motion in the horizontal direction is a uniform motion.
While the vertical and horizontal motions are independent, they occur simultaneously, which gives a projectile its characteristic curved parabolic path.
It’s essential to remember to consider direction when applying the equations of motion. Specifically, acceleration due to gravity is downwards, thus it is commonly assigned a negative value.
While air resistance is usually neglected in these calculations, in real-life situations it can have a considerable effect on the motion of a projectile.