Question - Calculating Time to Reach Maximum Height of Ball
Solution:
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.
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