Which angle gives the maximum range?

You can work it out this way: try angles between 30° and 60°.

Free~15 min

Projectile Motion

Launch, arc, and land

How it works

Projectile motion is the motion of an object thrown into the air, subject only to gravity. The horizontal and vertical components of motion are independent. The trajectory forms a parabola.

Step-by-step

Set the initial velocity and launch angle.
Press play to fire the projectile.
Observe the trajectory trace and compare range at different angles.

Key formulas

$x = v_0 \cos(\theta) \cdot t$ Horizontal position
$y = v_0 \sin(\theta) \cdot t - \frac{1}{2}gt^2$ Vertical position
$R = \frac{v_0^2 \sin(2\theta)}{g}$ Range
$H = \frac{(v_0 \sin\theta)^2}{2g}$ Max height

Frequently asked questions

Which angle gives the maximum range?: You can work it out this way: try angles between 30° and 60°.
What is the flight time for v₀=50 m/s at 30°?: T = 2v₀sin(θ)/g.
How does gravity on Mars (3.7 m/s²) affect the range?: Adjust the gravity slider.