What is the maximum height of the projectile modeled by h(t) = -16t^2 + 32t + 48

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Question: What is the maximum height of the projectile modeled by h(t) = -16t^2 + 32t + 48? (2023)

Options:

Correct Answer: 64

Exam Year: 2023

Solution:

The maximum height occurs at t = -b/(2a) = 1. h(1) = 64.

What is the maximum height of the projectile modeled by h(t) = -16t^2 + 32t + 48? (2023)

What is the maximum height of the projectile modeled by h(t) = -16t^2 + 32t + 48? (2023)

Step 1: Identify the equation of the projectile, which is h(t) = -16t^2 + 32t + 48.
Step 2: Recognize that this is a quadratic equation in the form h(t) = at^2 + bt + c, where a = -16, b = 32, and c = 48.
Step 3: To find the maximum height, use the formula for the time at which the maximum occurs: t = -b/(2a).
Step 4: Substitute the values of a and b into the formula: t = -32/(2 * -16).
Step 5: Calculate the value: t = -32 / -32 = 1.
Step 6: Now, substitute t = 1 back into the original equation to find the maximum height: h(1) = -16(1)^2 + 32(1) + 48.
Step 7: Calculate h(1): h(1) = -16(1) + 32 + 48 = -16 + 32 + 48.
Step 8: Simplify the calculation: h(1) = 16 + 48 = 64.
Step 9: Therefore, the maximum height of the projectile is 64.

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