Projectile Motion: Complementary Launch Angles

Theory

The motion splits in two: uniform horizontal motion $x=v_0\cos \theta t$ and uniformly accelerated vertical motion $y=v_0\sin \theta t-\frac{1}{2}g{t}^2$. The range on level ground is $R=\frac{v_0^2\sin 2\theta }{g}$ — maximum at 45° and equal for complementary angles (30° and 60°).

What to observe

• The dashed line is the trajectory predicted by theory (no air).
• Both cannonballs land at practically the same spot.

Try this

• Select a cannon and change its angle and speed.
• Turn on air resistance and compare with the prediction.

Also available in: Lançamento oblíquo: ângulos complementares (Português) · Movimiento parabólico: ángulos complementarios (Español)