Question

This is math homework, I don’t understand how to find the seconds after a balls hight

Answer 1

Substituting v₀=180 and h(t)=440 in the given equation we get:

`440=-16t^2+180t\text{.}`

Subtracting 440 from the above equation we get:

`\begin{gathered} 440-440=-16t^2+180t-440, \\ 0=-16t^2+180t-440. \end{gathered}`

Dividing the above equation by -2 we get:

`\begin{gathered} (0)/(-2)=(-16t^2+180t-440)/(-2), \\ 0=8t^2-90t+220. \end{gathered}`

Using the quadratic formula for second-degree equations we get:

`\begin{gathered} t=\frac{-(-90_{})\pm\sqrt[]{(-90)^2-4(8)(220)}}{2\cdot8}, \\ t=\frac{90\pm\sqrt[]{8100-7040}}{16}, \\ t=\frac{90\pm\sqrt[]{1060}}{16}, \\ t=\frac{90\pm2\sqrt[]{265}}{16}, \\ t=\frac{45\pm\sqrt[]{265}}{8}\text{.} \end{gathered}`

Therefore, the firework will reach a height of 440 feer after

`\begin{gathered} t=\frac{45-\sqrt[]{265}}{8}\approx(45-16.2788208)/(8) \\ =(28.7211794)/(8)=3.590147425\approx3.6. \end{gathered}`

seconds.

Answer: 3.6.

The number without being rounded yet is 3.590147425.