FREE TOOL · PHYSICS

Projectile Motion

Drag to aim, release to launch, then zoom into the arc. See range, peak height and flight time update as you play.

DRAG TO LAUNCH · LIVE READOUTS · NO SIGN-UP
01 · THE MODEL

Launch it. Watch the arc. Read the numbers.

Drag anywhere on the launcher to set the angle, or use the sliders below. Release to fire and the trajectory animates with a moving tracer point.

DRAG TO AIM RELEASE TO LAUNCH SCROLL TO ZOOM
Launch angle 45°
Launch speed 20 m/s
Gravity 9.8 m/s²
Projectile data 45° · 20 m/s
Range
40.8 m
Max height
10.2 m
Flight time
2.9 s
Vx (horizontal)
14.1 m/s
Vy (vertical)
14.1 m/s
Impact speed
20.0 m/s
Governing equations
R = v² sin(2θ) / g   ·   H = v² sin²θ / 2g   ·   T = 2v sinθ / g
02 · HOW TO USE

Everything responds to a drag or a click.

No hidden menus — the launch pad is the interface.

STEP 01

Aim the launcher

Click and drag anywhere on the stage to set the launch angle. The barrel, velocity vector and readout all update as you drag.

STEP 02

Release to fire

Let go to launch the projectile. The trajectory animates in real time with a glowing tracer point that leaves a fading tail.

STEP 03

Fine-tune with sliders

Use the angle, speed and gravity sliders for precise control, then hit Launch. Try changing gravity to see how the same launch behaves on the Moon or Jupiter.

STEP 04

Hover to inspect

Once the projectile is in the air, hover over the moving tracer to see live height and speed at that exact moment in the flight.

03 · READING THE DIAGRAM

What the arc is actually telling you.

The diagram is built to make three physical ideas visible at a glance.

Horizontal motion

x = vₓ · t

Once launched, there is no horizontal force (in ideal projectile motion), so the horizontal velocity stays constant. The projectile covers equal horizontal distances in equal times.

Vertical motion

y = v_y · t − ½ g t²

Gravity constantly accelerates the projectile downward. The vertical velocity decreases on the way up, reaches zero at the peak, then increases downward on the way back to the ground.

The parabola

y = x tanθ − (g x²) / (2 v² cos²θ)

Combining the two independent motions produces the familiar symmetric arc. The peak is exactly halfway through the flight time, and the path is perfectly mirrored on the way down.

04 · FAQ

Questions people actually ask.

The short answers — with the long ones one tap away.

What is projectile motion?+

Projectile motion is the curved path an object follows when it is thrown or launched and then moves only under the influence of gravity. The horizontal motion is constant velocity and the vertical motion is constant acceleration, and combining the two produces the familiar parabola.

What launch angle gives the maximum range?+

For a projectile launched and landing at the same height, the maximum range is achieved at a launch angle of 45°. Angles that are symmetric around 45° — such as 30° and 60° — give the same range, but the higher angle stays in the air longer.

How do you calculate the range of a projectile?+

For launch and landing at the same height the range is R = v² sin(2θ) / g, where v is the launch speed, θ is the launch angle and g is the acceleration due to gravity. Doubling the launch speed quadruples the range because range depends on the square of the speed.

What is the maximum height of a projectile?+

The maximum height is H = v² sin²θ / 2g. It depends only on the vertical component of the launch velocity, so a steeper launch angle gives a higher peak for the same speed.

How long does a projectile stay in the air?+

The total flight time is T = 2v sinθ / g for equal launch and landing heights. It is determined entirely by the vertical motion, so a larger vertical velocity component means a longer flight.

Does air resistance change projectile motion?+

Yes. In the real world air resistance shortens the range, lowers the maximum height and makes the path asymmetric, with a steeper descent than ascent. This tool models the ideal case with no air resistance, which is the standard first step taught in physics courses.

Is this tool free, and where does my data go?+

It's completely free and runs entirely in your browser — nothing you launch or click is uploaded, logged, or sent to any server. No account, no sign-up, no limits.