Question

a projectile is fired straight up from ground level with an initial velocity of 112 ft/s. its height, h, above the ground after t seconds is given by h = -16t² + 112t. what is the interval of time during which the projectiles height exceeds 192 feet? 3 < t < 4 1 < 4 1 > 4 3 > t > 4

Explanation:

Step1: Set up the inequality

We want to find when \(h=-16t^{2}+112t>192\). Rearrange it to \(16t^{2}-112t + 192<0\). Divide by 16: \(t^{2}-7t + 12<0\).

Step2: Factor the quadratic

Factor \(t^{2}-7t + 12=(t - 3)(t - 4)<0\).

Step3: Determine the interval

The roots of \(y=(t - 3)(t - 4)\) are \(t = 3\) and \(t = 4\). A quadratic \(y=ax^{2}+bx + c\) (\(a = 1>0\)) opens upwards. The inequality \((t - 3)(t - 4)<0\) holds when \(3

Answer:

\(3