Question

A ball is thrown upward from a height of 6 feet with an initial upward velocity of 24 ft/s. h(t)=−16t^2+24t+6. How long did it take to reach the maximum height (exact answer do not round)? t= seconds.

Answer 1

To find the time to reach maximum height for a ball thrown upward following the equation h(t)=-16t^2+24t+6, we calculate the vertex of the parabola, resulting in t = 0.75 seconds.

Step-by-step explanation:

The question concerns a ball being thrown upward with a known initial velocity and following a specific quadratic equation to describe its height over time. To find the time it takes to reach the maximum height, we need to find the vertex of the parabola represented by the quadratic equation h(t) = -16t^2 + 24t + 6. The vertex of a parabola y = ax^2 + bx + c occurs at t = -b/(2a). In this equation, a = -16 and b = 24, so the time at which the ball reaches its maximum height is t = -24 / (2 × -16), which simplifies to t = 0.75 seconds.