a rocket is launched into the air. the projectile motion of the rocket can be modeled using h(t) = 112t…

a rocket is launched into the air. the projectile motion of the rocket can be modeled using h(t) = 112t - 16t², where t is the time since launch in seconds and h(t) is the height of the rocket at time t. when will the rocket be 196 feet in the air? after 2.0 seconds after 3.5 seconds after 4.5 seconds after 7.0 seconds

a rocket is launched into the air. the projectile motion of the rocket can be modeled using h(t) = 112t - 16t², where t is the time since launch in seconds and h(t) is the height of the rocket at time t. when will the rocket be 196 feet in the air? after 2.0 seconds after 3.5 seconds after 4.5 seconds after 7.0 seconds

Answer

Explanation:

Step1: Set up the equation

Set $h(t)=196$, so $112t - 16t^{2}=196$.

Step2: Rearrange to standard - form

Rearrange to get $16t^{2}-112t + 196 = 0$. Divide through by 4: $4t^{2}-28t + 49 = 0$.

Step3: Use the quadratic formula

For a quadratic equation $ax^{2}+bx + c = 0$ ($a = 4$, $b=-28$, $c = 49$), the quadratic formula is $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. First, calculate the discriminant $\Delta=b^{2}-4ac=(-28)^{2}-4\times4\times49=784 - 784 = 0$. Then $t=\frac{28\pm\sqrt{0}}{8}=\frac{28}{8}=3.5$.

Answer:

after 3.5 seconds