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Virtual Labs · Interactive Physics

Projectile Motion Simulator

Change velocity, launch angle, gravity and initial height to see how each factor affects a projectile’s trajectory. Launch the simulation and explore projectile motion in real time.

010203040024681012Horizontal Distance (m)Height (m)45°LaunchPeak: 10.2 mRange: 40.8 m

Current state: time 0.00 seconds, horizontal position 0.00 metres, height 0.00 metres, speed 20.00 metres per second.

Launch Controls

m/s
1100
°
090
m/s²
125
m
0100

Results

Time of Flight
2.88 s
Maximum Height
10.19 m
Horizontal Range
40.77 m
Current Speed
20.00 m/s
Initial Vx
14.14 m/s
Initial Vy
14.14 m/s

How Projectile Motion Works

Projectile motion combines two completely independent motions happening at the same time. Ignoring air resistance, the horizontal motion moves at a constant velocity, while the vertical motion accelerates downward due to gravity. Neither motion affects the other — but together, they combine to trace out a smooth parabolic path.

Horizontal Motion (constant velocity)

Vx=ucos⁡θV_x = u\cos\theta
x(t)=ucos⁡θ⋅tx(t) = u\cos\theta \cdot t

Vertical Motion (accelerated by gravity)

Vy(t)=usin⁡θ−gtV_y(t) = u\sin\theta - gt
y(t)=h+usin⁡θ⋅t−12gt2y(t) = h + u\sin\theta \cdot t - \tfrac{1}{2}gt^2

Key Results

Range=u2sin⁡2θg\text{Range} = \dfrac{u^2\sin 2\theta}{g}Hmax=h+u2sin⁡2θ2gH_{max} = h + \dfrac{u^2\sin^2\theta}{2g}tflight=usin⁡θ+(usin⁡θ)2+2ghgt_{flight} = \dfrac{u\sin\theta + \sqrt{(u\sin\theta)^2 + 2gh}}{g}

How each parameter changes the trajectory

Increasing velocity

Generally increases both range and maximum height, since both depend on the square or product of the initial speed.

Increasing launch angle

Produces a steeper trajectory. When launch and landing heights are equal, the maximum range occurs at exactly 45°.

Increasing gravity

Decreases flight time, maximum height, and range — a stronger downward pull brings the projectile back down faster.

Increasing initial height

Gives the projectile extra time in the air before it reaches the ground, which generally increases its horizontal range.

Note: This simulator uses an idealized model with no air resistance. Real projectiles (like a thrown ball or a fired shell) experience drag, spin effects, and wind, which this model deliberately ignores to keep the underlying physics clear.

Try This

Short experiments to run in the simulator above — no answers given, just prompts to explore.

  • Set the angle to 30°. Note the range. Now change it to 60°. What do you notice about the two ranges when launch and landing heights are equal?
  • Keep the velocity and angle constant. Switch between Earth, Moon, and Jupiter. How does gravity change the trajectory shape, height, and flight time?
  • Set the initial height to 20 m. Compare the flight time and range with an identical launch from ground level (h = 0).
  • Try angles of 15° and 75°. Both give a smaller range than 45° — but do they give the same range as each other? Why might that be?
  • Set the launch angle to 90°. What happens to the horizontal range? Can you explain why using the velocity components?