🏀 Projectile Motion

📖 The Physics

Imagine throwing a ball. Two motions happen at the same time, and the key idea is that they don't affect each other. Sideways, nothing pushes the ball, so it keeps a constant horizontal speed. Downwards, gravity pulls it, so its vertical speed keeps changing — the ball slows as it rises, stops for an instant at the top, then speeds up as it falls. Adding these two motions together gives the familiar curved (parabolic) path.

We split the launch velocity into a horizontal part vₓ = v·cosθ and a vertical part v_y = v·sinθ, then handle each on its own. Here v is the launch speed, θ is the launch angle, and gis gravity.

Try setting the angle to 45° — for a given speed that gives the maximum range. Increasing gravity makes the ball fall faster, shrinking both the range and the flight time.