Newtonian mechanics

Projectile motion

Neglecting drag, projectile motion combines uniform horizontal motion with vertical motion accelerated by g.

A marble launched from a table edge keeps its horizontal velocity while gravity pulls it down, producing a parabolic path in the ideal model.

x = v₀ cosθ · t, y = y₀ + v₀ sinθ · t − ½gt²

Definition: Quantities and model

The horizontal component v₀cosθ stays constant; the initial vertical component is v₀sinθ and changes with acceleration −g (upward positive). These equations assume negligible drag and constant g.

Use the simulation to observe motion and read quantitative values as time evolves.

Reading the model

Neglecting drag, projectile motion combines uniform horizontal motion with vertical motion accelerated by g.

Example: Worked example

A projectile is launched horizontally at 4 m/s from height 5 m. With g = 10 m/s², fall time is √(2h/g) = 1 s and horizontal range is 4 m.

Solution

A projectile is launched horizontally at 4 m/s from height 5 m. With g = 10 m/s², fall time is √(2h/g) = 1 s and horizontal range is 4 m.

Resolve the launch velocity into $v_x=v_0cos heta$ and $v_y=v_0sin heta$ . With drag neglected, the horizontal component stays constant while gravity changes the vertical component; both motions share the same time. A horizontal launch at 6 m/s from 20 m, using $g=10 m/s²$ , lasts 2 s and travels 12 m horizontally.

Example: Range of a horizontal launch

A ball is launched horizontally at 8 m/s from 45 m. Take g=10 m/s². Find flight time and range.

Solution

t=√(2h/g)=3 s; x=vₓt=8×3=24 m.

At the highest point of an angled projectile’s path, its vertical velocity is momentarily zero but its horizontal velocity remains. The object therefore does not stop at the top. A parabolic path is a model assuming uniform gravity and negligible air resistance.

Quick check

Which quantity or statement is correct for this motion?

Which statement correctly describes the motion in this topic?

References

Young, Freedman (2019). University Physics
Halliday, Resnick, Walker (2014). Fundamentals of Physics