A polynomial models the height of a ball thrown from a height with an initial verti...
Check the final answer first, then review the worked steps.
Problem
A polynomial models the height of a ball thrown from a height with an initial vertical velocity. Identify the correct polynomial from given options.
Answer
\(-16t^2 + 30t + 6\)
Step-by-step solution
1. Identify the given polynomial model: The problem states that the polynomial $-16t^2 + vt + h_0$ models the height of a ball.
2. Identify the given values for velocity and initial height: The problem states that the initial vertical velocity ($v$) is 30 feet per second and the initial height ($h_0$) is 6 feet.
3. Substitute the given values into the polynomial: Replace $v$ with 30 and $h_0$ with 6 in the polynomial expression.
$$-16t^2 + (30)t + (6)$$
4. Simplify the expression: The expression becomes $-16t^2 + 30t + 6$.
5. Match with the given options: Compare the derived polynomial with the provided choices.