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-A foul tip of a baseball is hit straight upward from a height of 4 feet with an initial velocity of 112 feet per second. The function $s ( t ) = - 16 t ^ { 2 } + 112 t + 4$ describes the ball's height above the ground, s(t), in feet, $t$ seconds after it was hit. The ball reaches its maximum height above the ground when the instantaneous speed reaches zero. After how many seconds does the ball reach its maximum height?
A) 112
B) $\frac { 3 } { 32 }$
C) $\frac { 7 } { 2 }$
D) 7

Question

Quizplus · Accepted Answer

The maximum height of a projectile in motion, described by a quadratic equation of the form $s(t) = -16t^2 + vt + h$, is reached at $t = \frac{-b}{2a}$, where $a = -16$ and $b = 112$ in this case. Substituting these values gives $t = \frac{-112}{2(-16)} = \frac{112}{32} = \frac{7}{2}$ seconds.

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