The total time that Alice needs to hear the sound of hitting the water is equal to the sum of the time that the rock needs to hit the water and the time that the sound of hitting the water needs to return back to Alice. Let's first find the time that the rock needs to hit the water. We can find it from the kinematic equation:
here,
is the height of the bridge,
is the acceleration due to gravity, and
is the time that the rock needs to hit the water.
Then, from this formula we can find the time that the rock needs to hit the water:
Then, let's find the time that the sound of hitting the water needs to return back to Alice. We can find it from the equation:
here,
is the speed of sound,
is the time the sound of hitting the water needs to return back to Alice.
Then, we get:
Finally, we can find the total time that Alice needs to hear the sound of hitting the water:
Answer:
.
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