Question

A projectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = -16t2 + 704t. After how many seconds does the projectile take to reach its maximum height? Show your work for full credit.

Answer 1

The projectile reaches its maximum height after 22 seconds, which is determined by the vertex formula t = -b/(2a) applied to the given quadratic function representing the height over time.

Step-by-step explanation:

To determine after how many seconds the projectile reaches its maximum height, we need to analyze the function h(t) = -16t2 + 704t. This is a quadratic function, and the maximum height will be reached at the vertex of the parabola represented by this function.

The vertex of a parabola given by ax2 + bx + c can be found using the formula t = -b/(2a), where a, b, and c are coefficients from the quadratic equation. In this case, a = -16 and b = 704.

Using the formula to find the time t when the projectile reaches its maximum height, we calculate: t = -704/(2 × -16) = 704/32 = 22. Therefore, the projectile reaches its maximum height after 22 seconds.