A ball is thrown upward with an initial velocity of 49 m/s. Using the formula \(h(t) = -4.9t^2 + 49t\), what is the maximum height reached?

Thu, 07 May 2026 10:21:31 +0000

Maximum Height of a Ball Thrown Upward: A Physics Perspective Using the Quadratic Formula When a ball is thrown upward with an initial velocity of 49 meters per second, its height over time follows a quadratic trajectory governed by the equation: \\[
h(t) = -4.9t^2 + 49t
\\] This formula models the vertical position \\(h(t)\\) in meters as a function of time \\(t\\) in seconds. Because the coefficient of \\(t^2\\) is negative, the parabola opens downward, meaning the ball eventually rises to a peak and then falls back down — a classic example of projectile motion under gravity (with air resistance neglected).