It is given that the expression for the distance an object falls in t seconds is:
[tex]16t^2[/tex]It is required to find out if a rock that is 64 feet above water will hit the water in 2 seconds.
To do this, equate the distance above water to the expression given for distance:
[tex]16t^2=64[/tex]Next, solve the equation for t:
[tex]\begin{gathered} 16t^2=64 \\ \text{Divide both sides by 16:} \\ \Rightarrow\frac{16t^2}{16}=\frac{64}{16} \\ \Rightarrow t^2=4 \\ \Rightarrow t=\sqrt[]{4}=2 \end{gathered}[/tex]The time it will take for the object to fall a distance of 64 feet, is calculated to be 2 seconds.
This implies that if the rock is 64 feet from the water, it will hit the water in 2 seconds.
Yes, the rock will hit the water in 2 seconds.