Answer to Question #84401 in Physics for ciara

Question

Alice is standing on a bridge 112 m above a river. If she threw a rock over the edge, how long would it take for her to hear the sound of it hitting the water, assuming v sound = 330 m/s?

Answer 1

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:

$$h = \frac{1}{2}gt_{1}^2,$$

here,

$$h$$

is the height of the bridge,

$$g$$

is the acceleration due to gravity, and

$$t_{1}$$

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:

$$t_{1} = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \cdot 112 m}{9.8 \frac{m}{s^2}}} = 4.8 s.$$

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:

$$t_{2} = \frac{h}{v_{sound}},$$

here,

$$v_{sound}$$

is the speed of sound,

$$t_{2}$$

is the time the sound of hitting the water needs to return back to Alice.

Then, we get:

$$t_{2} = \frac{h}{v_{sound}} = \frac{112 m}{330 \frac{m}{s}} = 0.3 s.$$

Finally, we can find the total time that Alice needs to hear the sound of hitting the water:

$$t_{tot} = t_1 + t_2 = 4.8 s + 0.3 s = 5.1 s.$$

Answer:

$$t_{tot} = 5.1 s$$

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