Projectile Motion Simulator
Interactive physics simulation. Calculate trajectory, range, max height, and time of flight.
Visualize the physics of flight. Our **Projectile Motion Simulator** lets you see how launch angle, velocity, and height affect where a ball will land.
Launch Parameters
Trajectory Simulation
Flight Data
Max Height
10.19m
Range
40.77m
Time
2.88s
What is Projectile Motion Simulator?
What is Projectile Motion?
Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth's surface and moves along a curved path under the action of gravity only.
In this simulation, we ignore air resistance (drag), so the horizontal component of velocity remains constant, while the vertical component changes due to gravity ($g \approx 9.81 m/s^2$).
Formula & Calculation
The motion is split into two independent components: Horizontal (x) and Vertical (y).
Horizontal (x)
vₓ = v₀ · cos(θ)
x(t) = vₓ · t
No acceleration (aₓ = 0)
Vertical (y)
vᵧ = v₀ · sin(θ) - g·t
y(t) = h + vᵧ₀·t - ½gt²
Gravity acts downwards (aᵧ = -g)
Key Derived Formulas
- Range (R): $v^2 \sin(2\theta) / g$ (assuming launch from ground)
- Max Height (H): $v^2 \sin^2(\theta) / 2g$
- Time of Flight (T): $2v \sin(\theta) / g$
Example Calculation
The "Maximum Range" Problem
Question: At what angle should you throw a ball to make it go as far as possible (on flat ground)?
- Answer: 45 degrees.
- Reason: The range formula depends on $\sin(2\theta)$. Since the maximum value of sine is 1 (happening at 90°), we need $2\theta = 90^\circ$, so $\theta = 45^\circ$.
Try setting the angle to 45° in the simulator above and verify it gives the longest distance!
Frequently Asked Questions
Does mass matter?
In a vacuum (no air resistance), No. A feather and a bowling ball would follow the exact same path if launched at the same speed and angle. Gravity accelerates all objects equally regardless of mass.
Why is the path a parabola?
Because horizontal motion is linear (constant speed) and vertical motion is quadratic (due to gravity's acceleration), the combination creates a parabolic curve.