If you throw a ball in the air, what curve does it trace out?

If you throw a ball in the air, its ideal trajectory is a parabola.

This result comes from projectile motion. Ignoring air resistance and treating gravity as constant, the ball travels horizontally at a nearly constant speed while accelerating downward. Combining those two motions produces a curved path described mathematically by a quadratic equation, whose graph is a parabola.

Galileo Galilei established the parabolic shape of projectile paths in the early seventeenth century. The same model explains the flight of a thrown ball, the arc of a basketball, and the range of a kicked football. A launch angle of 45 degrees gives the greatest range when launch and landing heights are equal.

In real life, air drag, spin, changing wind, and Earth's curvature mean the path is not a perfect parabola. For ordinary throws over everyday distances, however, the parabolic approximation is highly accurate and is the standard physics answer.