Question

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?

Answer 1

It is given that the expression for the distance an object falls in t seconds is:

`16t^2`

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:

`16t^2=64`

Next, solve the equation for t:

`\begin{gathered} 16t^2=64 \\ \text{Divide both sides by 16:} \\ \Rightarrow(16t^2)/(16)=(64)/(16) \\ \Rightarrow t^2=4 \\ \Rightarrow t=\sqrt[]{4}=2 \end{gathered}`

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.