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 $h(t)=112t - 16t^{2}$, 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 $h(t)=112t - 16t^{2}$, 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: Establecer la ecuación

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

Step2: Re - escribir la ecuación en forma estándar

Reescribimos como $16t^{2}-112t + 196 = 0$. Dividimos entre 4: $4t^{2}-28t + 49 = 0$.

Step3: Aplicar la fórmula cuadrática

Para una ecuación $ax^{2}+bx + c = 0$, la fórmula cuadrática es $t=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Aquí $a = 4$, $b=-28$ y $c = 49$. Calculamos el discriminante $\Delta=b^{2}-4ac=(-28)^{2}-4\times4\times49=784 - 784=0$. Entonces $t=\frac{-(-28)\pm\sqrt{0}}{2\times4}=\frac{28}{8}=3.5$.

Answer:

after 3.5 seconds