Question

the height of a rocket a given number of seconds after it is released is modeled by h(t) = -16t² + 32t + 10. what does t represent?
○ the number of seconds after the rocket is released
○ the initial height of the rocket
○ the initial velocity of the rocket
○ the height of the rocket after t seconds

Explanation:

The function is \( h(t) = -16t^2 + 32t + 10 \), where \( h(t) \) represents the height of the rocket after \( t \) seconds. Let's analyze each option:

• Option 1: The problem states "a given number of seconds after it is released" and the function is in terms of \( t \), so \( t \) logically represents the number of seconds after release.
• Option 2: Initial height would be when \( t = 0 \), calculated as \( h(0)=10 \), not \( t \).
• Option 3: Initial velocity is related to the coefficient of \( t \) (derivative at \( t = 0 \)), not \( t \) itself.
• Option 4: \( h(t) \) is the height, not \( t \).

Answer:

A. the number of seconds after the rocket is released