A man drops a stone into a water well on
his farm. He hears the sound of the splash
3.55 s later.
How deep is the well? The acceleration due
to gravity is 9.8 m/s
2
and the speed of sound
in air is 324 m/s.
Answer in units of m
Vo= something
V= 324 m/s??
a= 9.8 m/s^2
t= 3.55 s
x= ?
To calculate the depth of the well, we can use the equation of motion for the stone that was dropped:
x = Vo*t + 0.5*a*t^2
In this equation,
- x represents the depth of the well (which we want to find)
- Vo is the initial velocity of the stone (which is 0, as it was dropped)
- t is the time taken for the stone to hit the water (given as 3.55 seconds)
- a is the acceleration due to gravity (given as 9.8 m/s^2)
Plugging in these values into the equation, we have:
x = 0*t + 0.5*(9.8)*(3.55)^2
x = 0 + 0.5*9.8*(12.6025)
x = 0 + 0.5*9.8*12.6025
x = 0 + 61.6095
x = 61.6095
Therefore, the depth of the well is approximately 61.61 meters.