Question

arthur drops a ball from a height of 81 feet above the ground. its height, (h), is given by the equation (h = -16t^2 + 81), where (t) is the time in seconds. for which interval of time is the height of the ball less than 17 feet?

(t > 2)
(0 < t < 2)
(t = 2)
(-2 < t < 2)

Explanation:

Set up the inequality

Using the Algebraic Modeling knowledge point

$$ -16t^2 + 81 < 17 $$

Solve the quadratic inequality

Using the Polynomial Inequalities knowledge point

$$
LATEXBLOCK0
$$

Apply physical constraints

Since time \(t\) represents the duration after the ball is dropped, we must have \(t \ge 0\). Therefore, the negative interval \(t < -2\) is physically impossible.

Thus, the valid time interval is:

$$ t > 2 $$

Answer:

• (A) \(t > 2\) (Correct answer)
• (B) \(0 < t < 2\)
• (C) \(t = 2\)
• (D) \(-2 < t < 2\)