Projectile Motion
Pick the angle and the speed. Where will the ball land?
Summary
The path of an object launched at an angle to the horizontal is called projectile motion. Without air resistance the path is a perfect parabola. Drag the arrow or use the sliders to change the speed and the angle; every launch leaves a trace on the screen, so you can compare which angle sends the ball the furthest.
In depth
Galileo Galilei solved projectile motion by separating the horizontal and vertical motions. Since no force acts horizontally, the horizontal velocity is constant (v₀·cos θ); vertically, gravity slows the object with a constant acceleration g, then pulls it back down. The combination of the two motions traces a parabola: y = x·tan θ − g·x² / (2v₀²·cos²θ). For an object launched and landing at the same height, the range is R = v₀²·sin(2θ)/g; it is largest at θ = 45°, and angles that add up to 90° (for example 30° and 60°) give the same range. If the launch point is above the ground or there is air resistance, the best angle drops below 45°.
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