Given:
The height of ball is represented by the below function:
[tex]h(t)=-16t^2+20t+24[/tex]
To find:
The number of seconds it will take to reach the ground.
Solution:
We have,
[tex]h(t)=-16t^2+20t+24[/tex]
At ground level, the height of ball is 0, i.e., [tex]h(t)=0[/tex].
[tex]-16t^2+20t+24=0[/tex]
Taking out greatest common factor.
[tex]-4(4t^2-5t-6)=0[/tex]
[tex]4t^2-5t-6=0[/tex]
Splitting the middle term, we get
[tex]4t^2-8t+3t-6=0[/tex]
[tex]4t(t-2)+3(t-2)=0[/tex]
[tex](t-2)(4t+3)=0[/tex]
Using zero product property, we get
[tex](t-2)=0[/tex] and [tex](4t+3)=0[/tex]
[tex]t=2[/tex] and [tex]t=-\dfrac{3}{4}[/tex]
Time cannot be negative, so [tex]t=2[/tex].
Therefore, the ball will reach the ground after 2 seconds.
