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

A ball is thrown straight upward from the top of $a=$ building with an initial velocity of 32 feet per second. The equation $s=-16 t^{2}+32 t+48$ gives the height $s$ of the ball in feet $t$ seconds after it is thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Solving Quadratic Equations

Solving quadratic equations is essential for determining key events in projectile motion, such as when an object reaches the ground. This is done by setting the quadratic expression equal to zero and applying methods like the quadratic formula, with attention given only to the physically meaningful (non-negative) solutions.

Vertex of a Parabola

The vertex of a parabola represents the maximum or minimum point of a quadratic function. In the context of projectile motion, when the quadratic function opens downward (indicating a negative acceleration due to gravity), the vertex gives the maximum height reached by the projectile. The time coordinate of the vertex is found using the formula -b/(2a).

Quadratic Functions

Quadratic functions are polynomial functions of degree two and are commonly written in the form ax^2 + bx + c. They model a variety of physical phenomena, including projectile motion, where the object’s path follows a parabolic curve due to constant acceleration, like gravity.

Transcript

Please give Ace some feedback