A stone is dropped from a tower 100 meters above the ground. The stone falls past ground level and into a well. It hits the water at the bottom of the well 5.00 seconds after being dropped from the tower. Calculate the depth of the well. Given: g = -9.81 meters/second2.
A.
22.5 meters
B.
50.7 meters
C.
100 meters
D.
110 meters
E.
152.45 meters
To solve this problem, we can use the equation of motion to determine the distance the stone traveled. The equation of motion is given by:
s = ut + (1/2)at^2
Where:
s = distance traveled
u = initial velocity (in this case, the stone is dropped, so the initial velocity is 0)
t = time taken
a = acceleration (in this case, acceleration due to gravity, which is -9.81 m/s^2)
Since the stone is dropped from rest, the initial velocity (u) is 0. Substituting the given values into the equation, we have:
s = 0 * t + (1/2) * (-9.81) * t^2
Simplifying the equation gives us:
s = (-4.905) * t^2
The stone hits the water at the bottom of the well after 5 seconds, so we can substitute t = 5 into the equation to find the distance traveled:
s = (-4.905) * (5)^2
s = (-4.905) * 25
s = -122.625
Now, the distance traveled (s) is negative because it is below the starting point. However, we want to find the depth of the well, which is a positive value. So we take the absolute value of s:
depth of well = |-122.625|
depth of well = 122.625 meters
Therefore, the depth of the well is 122.625 meters. Since none of the given answer choices matches exactly, we can round it to the nearest decimal place, which gives us:
Depth of the well = 122.6 meters
Therefore, the correct answer is not listed, but the closest option is:
B. 50.7 meters