Answer:
4 seconds
Step-by-step explanation:
[tex]h = -16t^2 + h_0[/tex]
where h=height reached after t seconds
[tex]h_0[/tex] = Initial Height of the ball
The ball is dropped from a height of 205 feet,
[tex]h_0[/tex] = 205 feet
We want to determine the time it takes the ball to reach the ground.
i.e. when height of the ball, h=0
Substituting [tex]h_0[/tex] = 205 feet and h=0 into the formula
[tex]h = -16t^2 + h_0[/tex]
[tex]0 = -16t^2 + 205[/tex]
Add [tex]16t^2[/tex] to both sides
[tex]0+16t^2 = -16t^2+16t^2 + 205\\16t^2=205[/tex]
Divide both sides by 16
[tex]\frac{16t^2}{16}= \frac{205}{16}\\t^2=12.8125[/tex]
[tex]t=\sqrt{12.8125} =3.58[/tex] ≈ 4 Seconds
It takes approximately 4 seconds for the ball to reach the ground.
