A ball is thrown upward from the top of a building. Its...

A ball is thrown upward from the top of a building. Its height $h,$ in feet, after $t$ seconds is given by the equation $h=-16 t^{2}+96 t+200 .$ How long will it take for the ball to be $88 \mathrm{ft}$ above the ground?

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Key Concepts

Projectile Motion

Projectile motion describes the motion of an object thrown into space under the influence of gravity, which imparts a constant acceleration. The object's trajectory in such cases is typically parabolic, and its vertical position can be modeled by a quadratic function over time, reflecting the effects of both initial velocity and gravitational acceleration.

Quadratic Equations

Quadratic equations are polynomial equations of degree two. They are fundamental in mathematics and arise naturally in many contexts, such as when modeling scenarios with constant acceleration. The general form ax² + bx + c = 0 can be solved using various techniques, including factoring, completing the square, or applying the quadratic formula.

Quadratic Formula

The quadratic formula, given by t = (-b ± ?(b² - 4ac))/(2a), is a key tool for solving quadratic equations. It provides the solutions for the variable in any quadratic equation, allowing one to determine the values of time or position in various physical and mathematical problems, especially in contexts like projectile motion.

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