Question - Calculating Time to Reach Maximum Height of Ball
Solution:
The question is asking for the time it takes for the ball to reach its maximum height when thrown upward. The given equation for the height h in feet at any time t in seconds is:h(t) = -16t^2 + 32t + 5To find the time when the ball reaches its maximum height, we need to determine the vertex of the parabolic function since the coefficient of the t^2 term is negative, indicating that the parabola is concave down and the vertex will give the maximum height.For a quadratic equation in the form of ax^2 + bx + c, the x-coordinate of the vertex (which gives us the time in our case) can be found using the formula:t = -b/(2a)In our equation, a = -16 and b = 32. So plugging these values into our formula:t = -32 / (2 * -16)t = -32 / -32t = 1Therefore, it takes 1 second for the ball to reach its maximum height.
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