Projectile Motion

Algebra 1 · Axiom Academy

Projectile Motion: The Thrown Ball Throw a ball straight up and one quadratic equation tells you exactly how high it goes and when it lands. You toss a ball up from 5 feet off the ground at 40 feet per second . Gravity takes over, and its height at any time t (in seconds) is the quadratic: Set how hard you throw it, hit Throw, and watch the flight play out. That curved path — up, peak, back down — is the parabola the equation draws. The very top of the flight is the parabola's vertex . Drag the launch speed and watch the peak ride along the curve — the math says it happens at t = v_0/32 , where the height is h_0 + v_0^2/64 . The ball lands when its height is zero — that's a root of the quadratic. Drag the speed and watch the landing time slide along: only the positive root is a real moment in the flight. One quadratic holds the whole story of a thrown ball: its vertex is the peak height, and its positive root is when it lands. From a basketball arc to a water fountain to a rocket's climb, h(t) = -16t^2 + v_0 t + h_0 — read its peak, read its roots — is the same equation underneath.

This is the written version of the interactive lesson above. See the full Algebra 1 course.