Answer:
After 2 seconds the ball will hit the ground.
Step-by-step explanation:
A ball is thrown from a height of 40 meters with an initial downward velocity of 10/ms .
The ball's height h (in meters) after t seconds is given by the function
[tex]h=40-10t-5t^2[/tex]
At ground level height of ball is 0.
[tex]0=40-10t-5t^2[/tex]
[tex]0=5(8-2t-t^2)[/tex]
Splitting the middle term.
[tex]0=5(8-4t+2t-t^2)[/tex]
[tex]0=5(4(2-t)+t(2-t))[/tex]
[tex]0=5(2-t)(4+t)[/tex]
Using zero product property we get
[tex]2-t=0\Rightarrow t=2[/tex]
[tex]4+t=0\Rightarrow t=-4[/tex]
The time can not be negative. So, the value of t is 2
Therefore after 2 seconds the ball will hit the ground.
