Calculating Time to Reach Maximum Height of Ball
To find out how long it takes for the ball to reach its maximum height, we need to analyze the given quadratic equation for height \( h \), which is:
\[ h(t) = -16t^2 + 32t + 5 \]
This is a quadratic equation in the standard form:
\[ h(t) = at^2 + bt + c \]
In this equation, \( h(t) \) represents the height of the ball at any time \( t \), measured in seconds. The ball will reach maximum height at the vertex of the parabola, which is given by the formula \( t = -\frac{b}{2a} \), where \( a \) and \( b \) are coefficients from the quadratic equation.
Here, \( a = -16 \) and \( b = 32 \), so let's calculate:
\[ t = -\frac{b}{2a} = -\frac{32}{2(-16)} = -\frac{32}{-32} = 1 \]
Therefore, the ball will reach its maximum height after 1 second.
