a projectile is fired straight up from ground level with an initial velocity of 112 ft/s. its height, h…

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 $h = -16t^2 + 112t$. what is the interval of time during which the projectiles height exceeds 192 feet?$\bigcirc$ $3 < t < 4$$\bigcirc$ $t < 4$$\bigcirc$ $t > 4$$\bigcirc$ $3 > t > 4$

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 $h = -16t^2 + 112t$. what is the interval of time during which the projectiles height exceeds 192 feet?$\bigcirc$ $3 < t < 4$$\bigcirc$ $t < 4$$\bigcirc$ $t > 4$$\bigcirc$ $3 > t > 4$

Answer

Explanation:

Step1: Set up inequality

$ -16t^2 + 112t > 192 $

Step2: Rearrange to standard form

$ -16t^2 + 112t - 192 > 0 $

Step3: Divide by -16 (reverse inequality)

$ t^2 - 7t + 12 < 0 $

Step4: Factor quadratic

$ (t-3)(t-4) < 0 $

Step5: Find critical points & test intervals

Critical points: $t=3, t=4$. The quadratic is negative between 3 and 4.

Answer:

3 < t < 4