Answer:
t = 8 seconds
Explanation:
Given the equation:
[tex]-4.9t^2+24.5t+117.6=0[/tex]First, multiply all through by 10 in order to change the decimals to whole numbers as it is easier to work with whole numbers.
[tex]\begin{gathered} 10(-4.9t^2+24.5t+117.6)=10\times0 \\ -49t^2+245t+1176=0 \end{gathered}[/tex]Next, factor out 49.
[tex]\implies49(-t^2+5t+24)=0[/tex]Divide both sides by 49:
[tex]\begin{gathered} \frac{49(-t^2+5t+24)}{49}=\frac{0}{49} \\ \implies-t^2+5t+24=0 \end{gathered}[/tex]So, we have succeeded in reducing the initial equation given to the form above.
Next, factorize to solve for t.
[tex]\begin{gathered} -t^2+5t+24=0 \\ -t^2+8t-3t+24=0 \\ -t(t-8)-3(t-8)=0 \\ (-t-3)(t-8)=0 \\ \implies-t-3=0\text{ or }t-8=0 \\ \implies t=-3=0\text{ or }t=8 \\ \text{But }t\neq-3 \\ \implies t=8\text{ seconds} \end{gathered}[/tex]The ball will hit the ground after 8 seconds.
