Question

Describe three factors those affect the trajectory of a projectile.

Hint:

In sports like Shot Put, where the release point is higher than the landing point, the optimal angle is actually slightly less than 45° (around 37°–42°).

Answer 1

Step 1: Understanding the Concept:
A projectile is any object thrown into space upon which the only acting force is gravity. Its path (trajectory) is parabolic.
Step 2: Detailed Explanation:

1. Angle of Projection: The angle at which the object is released. For maximum horizontal distance (range), the ideal angle is 45° (assuming release and landing heights are equal).
2. Initial Velocity: The speed at which the object is thrown. Higher initial velocity results in a longer and higher trajectory.
3. Gravity: Gravity pulls the projectile downward, causing the vertical component of the velocity to decrease. It is the force that turns a straight path into a curve.
Step 3: Final Answer:
The trajectory is influenced by the angle of release, the speed of release, and the force of gravity.

Answer 2

A projectile's path can be understood by breaking its motion into horizontal and vertical components and asking what changes each component. Doing this identifies the factors that shape the trajectory from a slightly different angle than listing them directly.

Initial speed and its two components: When a projectile is launched with speed \( u \) at angle \( \theta \), it has a horizontal component \( u\cos\theta \), constant throughout flight since gravity acts only vertically, and a vertical component \( u\sin\theta \), which determines how high and how long it stays in the air. A larger \( u \) increases both components, stretching the trajectory both further and higher.
Launch angle and how it splits speed between the two components: The angle \( \theta \) decides how the same initial speed is divided between horizontal reach and vertical height. A low angle sends more speed into the horizontal component, a flat, long trajectory, a high angle sends more into the vertical component, a short, tall trajectory, and \( 45^\circ \) balances the two to give the maximum horizontal range when launch and landing heights are equal, since range follows \( R = \dfrac{u^2 \sin(2\theta)}{g} \).
Gravity acting only on the vertical component: Because gravity \( g \) constantly decelerates the upward vertical motion and then accelerates the fall, it is solely responsible for curving what would otherwise be a straight-line path into the familiar parabolic arc, while leaving the horizontal component untouched.
Air resistance, in real, non-ideal conditions: Although idealised projectile motion problems ignore it, in practice air resistance opposes motion along the direction of travel, gradually reducing both components of velocity and shortening the trajectory compared to the ideal parabolic path.

Viewed this way, the trajectory is really shaped by how speed splits into horizontal and vertical components at launch, and by which forces then act on each of those components during flight.