Question

A projectile is fired straight up from ground level. After t seconds, its height above the ground is s feet, where s=-16t²+144t For what time period is the projectile at least 288 feet above the ground?

Answer 1

To find when the projectile is at least 288 feet above the ground, we solve the quadratic inequality -16t² + 144t ≥ 288. The quadratic formula gives us t = 3.79 s and t = 0.54 s. The projectile is at or above 288 feet between these two times.

Step-by-step explanation:

To determine the time period when the projectile is at least 288 feet above the ground, we need to solve the inequality -16t² + 144t ≥ 288.

First, we set up the equation:
-16t² + 144t - 288 = 0

Factoring or using the quadratic formula, we find the roots of the equation which are the times when the projectile is exactly 288 feet above the ground. These roots will determine the interval during which the projectile's height is at or above 288 feet. The inequality may yield two time values, which correspond to the time when the projectile is going up and when it is coming down.

Using the quadratic formula and the given values for the coefficients, we calculate the roots to be:

t = 3.79 s (on the way down)

t = 0.54 s (on the way up)

The projectile is at least 288 feet above ground between the times t = 0.54 s and t = 3.79 s.