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Due to gravity, an object falls 16t2 feet in t seconds. You drop a rock from a bridge that is 64 feet above the water. Will the rock hit the water in 2 seconds?

Due To Gravity An Object Falls 16t2 Feet In T Seconds You Drop A Rock From A Bridge That Is 64 Feet Above The Water Will The Rock Hit The Water In 2 Seconds class=

Sagot :

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.