a stone is dropped from rest at the top of a mine shaft. it takes 59 s for a stone to fall to the bottom of a mine shaft. how deep is the shaft? the acceleration of gravity is 9.8 m/s2

To find the depth of the mine shaft, we can use the equation of motion for an object in free fall:

d = (1/2) * g * t^2

where:
d = depth of the mine shaft
g = acceleration due to gravity (9.8 m/s^2)
t = time taken for the stone to fall (59 s)

Plugging in the values into the equation, we can calculate the depth of the mine shaft:

d = (1/2) * 9.8 m/s^2 * (59 s)^2
d = (1/2) * 9.8 m/s^2 * 3481 s^2
d = 17,060.9 m^2/s^2

Therefore, the depth of the mine shaft is approximately 17,060.9 meters.

To find the depth of the mine shaft, we can use the equation of motion for an object in free fall:

h = (1/2) * g * t^2

Where:
h = depth of the mine shaft
g = acceleration due to gravity (9.8 m/s^2)
t = time taken for the stone to fall (59 s)

Substituting the given values into the equation, we get:

h = (1/2) * 9.8 * (59)^2

First, let's square the value of 59:

h = (1/2) * 9.8 * 3481

Then, multiply 9.8 by 3481:

h = 17135.9 m

Rounding to the appropriate number of significant figures, the depth of the mine shaft is approximately 17136 m.