Explanation 1) Concept: The maximum height of the projectile is the maximum value of h ( t ) . The graphical representation of the function h ( t ) = − 16 t 2 + 96 t is a parabola. The coefficient of t 2 is negative. Therefore, it is a parabola that opens downward. So, the h ( t ) or the y co-ordinate of the vertex gives the maximum height. Step 1: Compare h ( t ) with the general quadratic equation f ( x ) = a x 2 + b x + c . Find the values of a and b . Step 2: Find the vertex using the formula ( − b 2 a , h ( − b 2 a ) ) . Step 3: The x co-ordinate of the vertex is the numbers of seconds the projectile takes to reach the maximum height and the y co-ordinate of the vertex is the maximum height of the projectile. 2) Calculation: Comparing h ( t ) = − 16 t 2 + 96 t with f ( x ) = a x 2 + b x + c , we have a = − 16 ; b = 96 ; Now, to find the x co-ordinate of the vertex, substitute the values of a and b in − b 2 a

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Author: Elayn Martin-Gay

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Chapter 11.6, Problem 55E

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If a projectile is fired straight upward from the ground with an initial speed of 96 feet per second, then its height h in feet after t seconds is given by the equation h(t)=−16t2+96t. Find the maximum height of the projectile.

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Chapter 11.6, Problem 54E

Chapter 11.6, Problem 56E

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Chapter 11 Solutions

Pearson eText for Beginning & Intermediate Algebra -- Instant Access (Pearson+)

Ch. 11.1 - Prob. 1G Ch. 11.1 - Prob. 2G Ch. 11.1 - Prob. 3G Ch. 11.1 - Prob. 4G Ch. 11.1 - Prob. 5G Ch. 11.1 - Prob. 6G Ch. 11.1 - Prob. 1P Ch. 11.1 - Prob. 2P Ch. 11.1 - Prob. 3P Ch. 11.1 - Prob. 4P

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To Answer: If a projectile is fired straight upward from the ground with an initial speed of 96 feet per second, then its height h in feet after t seconds is given by the equation h ( t ) = − 16 t 2 + 96 t . Find the maximum height of the projectile.

To Answer: If a projectile is fired straight upward from the ground with an initial speed of 96 feet per second, then its height h in feet after t seconds is given by the equation h(t)=−16t2+96t. Find the maximum height of the projectile.

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Chapter 11 Solutions

To Answer:

If a projectile is fired straight upward from the ground with an initial speed of 96 feet per second, then its height h in feet after t seconds is given by the equation h(t)=−16t2+96t. Find the maximum height of the projectile.