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By the end of this topic, you should be able to:
Model the motion of a projectile as a particle moving with constant acceleration and understand any limitations of the model.
Use horizontal and vertical equations of motion to solve problems on the motion of projectiles, including finding the magnitude and direction of the velocity at a given time or position, the range on a horizontal plane and the greatest height reached.
Derive and use the Cartesian equation of the trajectory of a projectile, including problems in which the initial speed and/or angle of projection may be unknown.
A projectile is any object that is thrown, launched, or projected into the air and then moves under the influence of gravity alone. Examples include a ball thrown by a cricketer, a stone kicked off a cliff, or a water fountain jet.
We model a projectile as a particle (a single point with mass but no size) that moves with constant acceleration due to gravity.
Key assumptions of the model:
Gravity is constant: We assume gravity pulls the projectile downward with a constant acceleration of g = 9.8 m/s² (or sometimes approximated as 10 m/s² for simpler calculations).
No air resistance: We ignore the effects of air pushing against the projectile as it moves.
The projectile is a particle: We treat it as a tiny point, ignoring its size, shape, and rotation.
Motion happens near Earth's surface: The ground is flat and horizontal.
The model is useful but not perfect. Here are its limitations (situations where the model doesn't work well):
Air resistance matters for light or fast objects: A feather, a parachute, or a speeding bullet experiences significant air resistance, which we're ignoring.
Gravity isn't perfectly constant: If the projectile travels very high or very far, the strength of gravity changes slightly. Our model assumes it stays the same.
The projectile has size and spin: Real objects like footballs or frisbees experience effects due to their shape and spin. Our particle model ignores these.
Earth's curvature: For very long-range projectiles (like missiles), the Earth's curve matters. We assume a flat surface.
In summary: The model works well for everyday situations like throwing a ball across a field, but not for extreme cases like skydiving or rocket launches.
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