Question

the height of a rocket a given number of seconds after it is released is modeled by $h(t) = -16t^2 + 32t + 10$. 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 1 seconds

Explanation:

The function \( h(t) = -16t^2 + 32t + 10 \) models the height of the rocket. In such a context, the variable \( t \) in the function's argument typically represents the independent variable related to time. The problem states "a given number of seconds after it is released", so \( t \) should represent the number of seconds after the rocket is released. The initial height would be \( h(0) \), initial velocity is related to the coefficient of \( t \) (not \( t \) itself), and \( h(t) \) is the height after \( t \) seconds (not \( t \) representing height).

Answer:

A. the number of seconds after the rocket is released