A physics student drops a physics text book into a mine shaft 250m deep,where the average mine temperature is 5degrees celsius.Show that the sound of the book striking the bottom is heard after 7.82seconds
d = Vo*t + 4.9*t^2 = 250 m.
0 + 4.9t^2 = 250.
t^2 = 250 / 4.9 = 51.0.
Tf = 7.14 s. = Fall time.
d = V*T.
T = d/V = 250m / 343m/s = 0.729 s. =
Time for sound to travel 250 meters up.
Tf + T = 7.14 + 0.729 = 7.87 s.
To determine the time it takes for the sound of the book striking the bottom of the mine shaft to reach the surface, we can use the speed of sound in air.
The speed of sound in air depends on the temperature of the air. The formula to calculate the speed of sound in air is:
v = 331.4 + 0.6 * T
Where:
- v is the speed of sound in m/s
- T is the temperature in °C
In this case, the temperature in the mine shaft is given as 5°C. So, we can calculate the speed of sound in air as follows:
v = 331.4 + 0.6 * 5
v = 331.4 + 3
v = 334.4 m/s
Now, we need to calculate the time it takes for the sound to travel 250m (the depth of the mine shaft). We can use the equation:
time = distance / speed
Substituting the values:
time = 250 / 334.4
time ≈ 0.747 seconds
Therefore, the sound of the book striking the bottom of the mine shaft would be heard after approximately 0.747 seconds.
Note: It seems that the given value of 7.82 seconds is incorrect. The correct time would be much shorter, as calculated above.