Question 13.
Given:
Height = 144 feet.
Let's determine how many seconds it will take for a ball dropped from a window of the given height to hit the ground.
Here, we have the equation:
[tex]y=-16x^2+144[/tex]
Where:
y represents the height of the ball after x seconds.
Now, when the ball hits the ground, the height will be 0 ft.
Thus, to find the time at 0 ft, substitute 0 for y and solve for x:
[tex]\begin{gathered} 0=-16x^2+144 \\ \\ 16x^2=144 \end{gathered}[/tex]
Divide both sides by 16:
[tex]\begin{gathered} \frac{16x^2}{16}=\frac{144}{16} \\ \\ x^2=9 \end{gathered}[/tex]
Take the square root of both sides:
[tex]\begin{gathered} \sqrt{x^2}=\sqrt{9} \\ \\ x=3 \end{gathered}[/tex]
Therefore, it will take the ball 3 seconds to hit the ground.
ANSWER:
• (a). y = -16t² + 144
• (b). 3 seconds
