Question

Got stuck on this question, need help with other steps

Answer 1

the object will hit the ground at 4.793 seonds

Explanation

Given the function below

`s(t)=-16t^2\text{ + 60t + 80}`

To find the value of t in seconds, let s(t) = 0

The new equation becomes

`-16t^2\text{ + 60t + 80 = 0}`

The quadratic function can be solved using the general quadratic formula

From the equation above,

Let a = -16, b = 60, and c = 80

`\begin{gathered} t\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ t\text{ = }\frac{-(60)\pm\sqrt[]{60^2\text{ - 4 (-16)(80)}}}{2\text{ (-16)}} \\ t\text{ = }\frac{-60\pm\sqrt[]{3600\text{ + 5120}}}{-32} \\ t\text{ = }\frac{-60\text{ }\pm\sqrt[]{8720}}{-32} \\ t\text{ = }(-60\pm93.38)/(-32) \\ t\text{ = }\frac{-60\text{ + 93.38}}{-32}\text{ or }\frac{-60\text{ - 93.38}}{-32} \\ t\text{ = }(33.38)/(-32)\text{ or }(-153.8)/(-32) \\ t\text{ = -1.043 seconds or 4.793 secons} \end{gathered}`

Hence, the object will hit the ground at 4.793 seonds