Answer:
Therefore,
The ball strike the ground at time , t = 6 s
Step-by-step explanation:
Given:
The equation for the ball’s height, h, at time t seconds is
![h=-4.9t^{2}+19.6t+58.8](https://tex.z-dn.net/?f=h%3D-4.9t%5E%7B2%7D%2B19.6t%2B58.8)
To Find:
time, t = ? (When the ball strike the ground)
Solution:
When the ball strike the ground height, h will be ZERO,
So put h = 0 in above given equation for time,
![0=-4.9t^{2}+19.6t+58.8](https://tex.z-dn.net/?f=0%3D-4.9t%5E%7B2%7D%2B19.6t%2B58.8)
Which is a Quadratic Equation
Dividing throughout by - 4.9 we get
![0=t^{2}-4t-12](https://tex.z-dn.net/?f=0%3Dt%5E%7B2%7D-4t-12)
On Factorizing, splitting the middle term we get
![t^{2}-6t+4t-12=0](https://tex.z-dn.net/?f=t%5E%7B2%7D-6t%2B4t-12%3D0)
![t(t-6)+2(t-6)=0\\\\(t+2)(t-6)=0\\\\t=-2\ or\ t=6](https://tex.z-dn.net/?f=t%28t-6%29%2B2%28t-6%29%3D0%5C%5C%5C%5C%28t%2B2%29%28t-6%29%3D0%5C%5C%5C%5Ct%3D-2%5C%20or%5C%20t%3D6)
As time cannot be negative,
t = 6 s
Therefore,
The ball strike the ground at time , t = 6 s