If a ball is thrown directly upward with a velocity of 40 ft / s, its height (in feet) after t s

step 1 So in this question, a ball is being thrown upwards, and its height in feet after T seconds is g

If a ball is thrown directly upward with a velocity of 40 ft...

If a ball is thrown directly upward with a velocity of $40 \mathrm{ft} / \mathrm{s}$, its height (in feet) after $t$ seconds is given by $y=40 t-16 t^2$. What is the maximum height attained by the ball?

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Key Concepts

Quadratic Functions

Quadratic functions are equations of the form y = ax² + bx + c, where the graph is a parabola. They model situations where a quantity changes in a non-linear way, and in the context of motion, they describe trajectories under constant acceleration.

Projectile Motion

Projectile motion involves objects moving under the influence of gravity, where the vertical component of the motion is described by a quadratic function. It combines the initial velocity and gravitational acceleration to determine the object's height at any given time.

Vertex of a Parabola

The vertex of a parabola is the highest or lowest point on its graph, depending on the orientation of the parabola. In problems where the quadratic function represents height, the vertex indicates the maximum height attained, and it is calculated using the formula t = -b/(2a).

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