Respuesta :
The total time in seconds the ball will take to travel before returning the ground is 2.25 seconds.
What is factorisation?
The breaking or breakdown of an entity (such as an integer, a matrices, or a polynomials) into a products of another unit, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring in mathematics.
Calculation for the time;
Let 't' be the time in second the ball will travel.
Let H(t) be the total height travelled by the ball.
The equation of the height is given as
[tex]H(t)=-16 t^{2}+36 t[/tex]
As soon as the ball will return to the ground the total height will become zero.
So, put equation of height equal to zero.
[tex]-16 t^{2}+36 t=0[/tex]
Factorise the above equation;
[tex]-16 t\left(t-\frac{9}{4}\right)=0[/tex]
Put each value equals to zero to get the value of time.
[tex]\begin{aligned}&t=0 \mathrm{sec} \\&t=9 / 4=2.25 \mathrm{sec}\end{aligned}[/tex]
As, time can not be zero
Therefore, the total time taken by the ball to return to the ground is 2.25 sec.
To know more about factorisation, here
https://brainly.com/question/25829061
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