All courses › Foundations of Physics › Projectile motion

Projectile motion

When something is thrown at an angle, the motion splits into a horizontal part with constant velocity and a vertical part with free fall. The two directions do not affect each other, so you solve them separately and connect them only through the time $t$ .

x = v_0\cos\theta\cdot t

horizontal position

y = v_0\sin\theta\cdot t - \tfrac12 gt^2

vertical position (upward positive)

Symbols

$v_0$	initial speed	m/s
$\theta$	launch angle	°
$x,\ y$	horizontal/vertical position	m

Example

A ball is thrown at $v_0 = 15$ m/s at $\theta = 30^\circ$ . Horizontal component: $v_0\cos 30^\circ \approx 13$ m/s. After $t = 1.0$ s: $x \approx 13$ m.

Always split into an x- and a y-component first – time is the only thing that connects them.

Practise motion for free →

← Free fall · Newton's laws →

Part of Foundations of Physics: Motion.