Physics · Interactive
Projectile Motion
A projectile launched into the air traces a parabolic arc under gravity. Drag the launch angle and initial speed below to reshape the trajectory and watch the range, maximum height, and time of flight update live. Free to use, and exportable into your slides.
Drag the launch angle and speed to reshape the arc. Open fullscreen ↗
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What is projectile motion?
Projectile motion is the curved path an object follows when it is launched into the air and moves under gravity alone, with no air resistance. The motion splits into two independent parts: horizontal motion at constant velocity, and vertical motion with constant downward acceleration from gravity. Combining them produces the familiar parabolic arc. Drag the launch angle and initial speed in the simulator above to reshape that arc.
Horizontal and vertical components
A launch speed v₀ at angle θ is split into a horizontal component vₓ = v₀·cos(θ) and a vertical component v_y = v₀·sin(θ). The horizontal component stays constant for the whole flight, so it sets how far the projectile travels. The vertical component starts positive, slows to zero at the top of the arc, then reverses as the object falls. The simulator reports both components as you change the angle and speed.
Range, maximum height, and time of flight
For a projectile launched from ground level, the range is R = v₀²·sin(2θ) / g, the maximum height is H = (v₀·sin θ)² / (2g), and the time of flight is T = 2·v₀·sin θ / g, where g is 9.8 m/s². The range is largest at a 45 degree launch angle, and complementary angles such as 30 and 60 degrees give the same range. Watch these values update live in the panel as you drag the sliders.
Why the path is a parabola
Because the horizontal position grows steadily while the vertical position follows a constant-acceleration equation, eliminating time between the two gives an equation of the form y = ax² + bx, which is a parabola. That is why every ideal projectile, from a thrown ball to a launched cannonball, traces a symmetric parabolic arc that rises to a peak and falls back down over an equal horizontal distance.
Frequently asked questions
What is projectile motion?
Projectile motion is the motion of an object thrown or launched into the air, moving under gravity alone. It combines constant horizontal velocity with constant vertical acceleration, tracing a parabolic path.
What launch angle gives the maximum range?
On level ground with no air resistance, a launch angle of 45 degrees gives the maximum range for a given speed. Angles that add up to 90 degrees, such as 30 and 60, produce the same range.
How do you calculate the range of a projectile?
For a launch from ground level, the range is R = v₀²·sin(2θ) / g, where v₀ is the initial speed, θ is the launch angle, and g is the acceleration due to gravity (9.8 m/s²).
How do you find the maximum height?
The maximum height is H = (v₀·sin θ)² / (2g). It depends only on the vertical component of the initial velocity, so a steeper launch angle reaches a higher peak.
Why is the path of a projectile a parabola?
Horizontal position increases at a constant rate while vertical position follows a constant-acceleration equation. Eliminating time between them gives a quadratic relation y = ax² + bx, which graphs as a parabola.
How do I use this projectile motion simulator?
Drag the launch angle and initial speed sliders. The trajectory redraws instantly, the apex and landing point are marked, and the panel shows the range, maximum height, time of flight, and velocity components. You can also export the graph.