Question

The time it takes for the ball to strike the ground is about? and is it feet , seconds or feet per second

Answer 1

2.6 seconds

Step-by-step explanation

we have

`\begin{gathered} h(t)=-16t^2-12t+140 \\ where\text{ t is the time ( in seconds)} \\ h\text{ is the height ( in f}eet) \end{gathered}`

so, to knowe the time when the ball hits the ground we need to set the function equals zero and solve for t

hence

`\begin{gathered} h(t)=-16t^2-12t+140 \\ \text{the ball hits the ground when heigth = 0 , h=0} \\ \text{replace} \\ 0=-16t^2-12t+140 \\ -16t^2-12t+140=0\rightarrow equation \end{gathered}`

Step 2

use the quadratic formula to solve the equation:

the quadratic formula says

`\begin{gathered} \text{for} \\ ax^2+bx+c=0 \\ the\text{ solution for x is} \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}`

so

let

`\begin{gathered} -16t^2-12t+140=0\rightarrow ax^2+bx+c \\ so \\ a=-16 \\ b=-12 \\ c=140 \\ \text{replace in the formula} \\ t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t=\frac{-(-12)\pm\sqrt[]{(-12)^2-4\cdot-16\cdot140}}{2\cdot-16} \\ t=(12\pm95.41)/(-32) \\ so \\ t_1=(12+95.41)/(-32)=\cdot-3.35s \\ t_1=(12-95.41)/(-32)=2.606\text{ s} \\ so\text{, the time is} \\ t=2.6\sec onds \end{gathered}`

so, the answer is

2.6 seconds

I hope this helps you