At max height, v = 0 → use v² = u² − 2gh → 0 = 30² − 2×9.8×h → h = 900 / 19.6 ≈ <<900/19.6=45.92>>45.92 m

["How Maximum Height is Calculated in Free Fall: A Step-by-Step Explanation Using Physics", "When an object is thrown vertically upward, it eventually stops at its maximum height—just before falling back down. Understanding how to calculate this height is essential in kinematics and helps clarify fundamental physics concepts like motion under gravity. One key formula used in this analysis is:", "[\nv^2 = u^2 - 2gh\n]", "At the peak of its trajectory, the final velocity ( v ) is zero because the object momentarily stands still before gravity pulls it back down. Substituting ( v = 0 ) into the equation simplifies it to:", "[\n0 = u^2 - 2gh\n]", "Rearranging gives:", "[\nu^2 = 2gh\n]", "Solving for height ( h ), we get:", "[\nh = \frac{u^2}{2g}\n]", "Let’s apply this to a classic example: imagine launching a ball upward with an initial velocity of ( u = 30 , \ ext{m/s} ), under Earth’s gravitational acceleration ( g = 9.8 , \ ext{m/s}^2 ). Plugging in these values:", "[\nh = \frac{30^2}{2 \ imes 9.8} = \frac{900}{19.6} \approx 45.92 , \ ext{meters}\n]", "So, the ball reaches a maximum height of about 45.92 meters before beginning its descent.", "This calculation is not only useful for physics students but also forms the foundation for real-world applications—from projectile motion in sports to engineering safety calculations. Understanding how to derive maximum height using kinematic equations empowers anyone working with vertical motion under gravity.", "Whether you’re studying physics, preparing for exams, or simply curious about motion, mastering this formula helps unlock deeper insights into the forces that govern our everyday world."]