QuestionJune 9, 2025

Steven decided to take his sling shot and send up a projectile at a speed of 290 feet per second straight upward Using the following equation below, what is the maximum height of the projectile? Round answer to nearest Hundreth of a foot. h(t)=-16t^2+290t+5

Steven decided to take his sling shot and send up a projectile at a speed of 290 feet per second straight upward Using the following equation below, what is the maximum height of the projectile? Round answer to nearest Hundreth of a foot. h(t)=-16t^2+290t+5
Steven decided to take his sling shot and send up a projectile at a speed of 290 feet per
second straight upward Using the following equation below, what is the maximum height
of the projectile? Round answer to nearest Hundreth of a foot.
h(t)=-16t^2+290t+5

Solution
4.7(281 votes)

Answer

1330.88 feet Explanation 1. Identify the Vertex of the Parabola The maximum height is at the vertex of the parabola. For h(t) = -16t^2 + 290t + 5, use the formula for the time at the vertex t = \frac{-b}{2a}, where a = -16 and b = 290. 2. Calculate Time at Maximum Height t = \frac{-290}{2(-16)} = \frac{290}{32} = 9.0625 seconds. 3. Calculate Maximum Height Substitute t = 9.0625 into h(t): h(9.0625) = -16(9.0625)^2 + 290(9.0625) + 5. 4. Simplify the Expression h(9.0625) = -16(82.015625) + 290(9.0625) + 5 = -1312.25 + 2638.125 + 5. 5. Compute Final Value h(9.0625) = 1330.875 feet.

Explanation

1. Identify the Vertex of the Parabola<br /> The maximum height is at the vertex of the parabola. For $h(t) = -16t^2 + 290t + 5$, use the formula for the time at the vertex $t = \frac{-b}{2a}$, where $a = -16$ and $b = 290$.<br /><br />2. Calculate Time at Maximum Height<br /> $t = \frac{-290}{2(-16)} = \frac{290}{32} = 9.0625$ seconds.<br /><br />3. Calculate Maximum Height<br /> Substitute $t = 9.0625$ into $h(t)$: <br /> $h(9.0625) = -16(9.0625)^2 + 290(9.0625) + 5$.<br /><br />4. Simplify the Expression<br /> $h(9.0625) = -16(82.015625) + 290(9.0625) + 5 = -1312.25 + 2638.125 + 5$.<br /><br />5. Compute Final Value<br /> $h(9.0625) = 1330.875$ feet.
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