Answer: Yes
Explanation:
To determine whether the rock will hit the water in 2 seconds, let's first analyze the motion of the falling object using the given information.
The equation for the displacement of an object in free fall is given by:
s = 16t^2
Where s represents the vertical displacement and t represents time.
In this case, the rock is dropped from a height of 64 feet above the water, so the equation becomes:
s = 64 - 16t^2
Here, s represents the displacement relative to the starting point, which is the height of the bridge.
To determine if the rock will hit the water in 2 seconds, we need to calculate the displacement of the rock at that time. Let's substitute t = 2 into the equation:
s = 64 - 16(2)^2
s = 64 - 16(4)
s = 64 - 64
s = 0
The result shows that at t = 2 seconds, the displacement of the rock is 0. This means that the rock has fallen exactly to the height of the water. Therefore, the rock will indeed hit the water in 2 seconds.