Calculating Time to Reach Maximum Height of a Ball
To solve for the time it takes for the ball to reach its maximum height, we can look at the equation of motion that is given:
\[ h = -16t^2 + 32t + 5 \]
In this equation, \(h\) represents the height of the ball in feet after \( t \) seconds.
The maximum height is reached at the vertex of the parabola represented by this quadratic equation. The time at which the maximum height is achieved can be found by using the formula \( t = -\frac{b}{2a} \), where \( a \) is the coefficient of \( t^2 \) and \( b \) is the coefficient of \( t \).
In this equation, \( a = -16 \) and \( b = 32 \). Plugging these values into the formula gives us:
\[ t = -\frac{32}{2(-16)} \]
\[ t = -\frac{32}{-32} \]
\[ t = 1 \]
So, it takes 1 second for the ball to reach its maximum height.
