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?
o 3<t<4
o t<4
o t>4
o 3>t>4

Explanation:

Step1: Set up the inequality

We want to find when $h>192$, so we set up the inequality $- 16t^{2}+112t>192$. Rearrange it to $16t^{2}-112t + 192<0$. Divide through by 16 to get $t^{2}-7t + 12<0$.

Step2: Factor the quadratic

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

Step3: Find the roots

Set $(t - 3)(t - 4)=0$. The roots are $t = 3$ and $t = 4$.

Step4: Determine the solution interval

For a quadratic $y=(t - 3)(t - 4)$ which is a parabola opening upwards (since the coefficient of $t^{2}$ is positive), the inequality $(t - 3)(t - 4)<0$ is satisfied when $3

Answer:

$3