Let's analyze the given polynomial [tex]\( h(t) = -16t^2 + 32t + 10 \)[/tex] to determine what each part represents:
1. The variable [tex]\( t \)[/tex]:
- In the context of this problem, [tex]\( t \)[/tex] is the independent variable in the function [tex]\( h(t) \)[/tex]. It typically represents the parameter which changes over time in such physics problems. Specifically, [tex]\( t \)[/tex] represents the number of seconds after the rocket is released. This is deduced from the standard form of kinematic equations where time is the variable.
2. The constants and coefficients in the polynomial:
- The constant term (10): This is the height of the rocket when [tex]\( t = 0 \)[/tex] (at the initial moment). Hence, it is the initial height of the rocket, which is 10 feet.
- The coefficient of the [tex]\( t \)[/tex] term (32): This represents the initial velocity of the rocket in the vertical direction, given in feet per second.
- The coefficient of the [tex]\( t^2 \)[/tex] term (-16): This is related to the acceleration due to gravity, but this is not directly asked in the question.
3. The function [tex]\( h(t) \)[/tex]:
- This function provides the height of the rocket after [tex]\( t \)[/tex] seconds. When you substitute a value of [tex]\( t \)[/tex] into this function, it gives you the corresponding height of the rocket at that specific time.
Given these explanations, the answer is:
- What does [tex]\( t \)[/tex] represent?
[tex]\( t \)[/tex] represents the number of seconds after the rocket is released.
Therefore, the correct answer is:
- the number of seconds after the rocket is released
