a stone is dropped down a well if it takes 5s to reach the surface of the water calculate how deep the well is , what is the velocity when it reaches the surface of the water
d = 0.5g*t^2.
g = 9.8 m/s^2, t = 5s.
V = Vo + g*t.
Vo = 0, g = 9.8, t = 5s.
To determine the depth of the well and the velocity of the stone when it reaches the surface of the water, we can use the following equations of motion:
1. Distance (d) = Initial velocity (u) * time (t) + 0.5 * acceleration (a) * time squared (t^2)
2. Final velocity (v) = Initial velocity (u) + acceleration (a) * time (t)
Since the stone is dropped, its initial velocity (u) is 0.
Step 1: Calculate the depth of the well (d):
Using equation 1, we can rearrange it to solve for distance (d):
d = 0 + 0.5 * 9.8 m/s^2 * (5s)^2
d = 0 + 0.5 * 9.8 m/s^2 * 25s^2
d = 0 + 122.5 m
d = 122.5 m
Therefore, the depth of the well is 122.5 meters.
Step 2: Calculate the velocity of the stone (v) when it reaches the water's surface:
Using equation 2, we have:
v = 0 + 9.8 m/s^2 * 5s
v = 0 + 49 m/s
Therefore, the velocity of the stone when it reaches the surface of the water is 49 m/s.
To calculate the depth of the well, we can use the equation of motion for free fall:
h = 1/2 * g * t^2
where:
- h is the depth of the well,
- g is the acceleration due to gravity (approximately 9.8 m/s^2),
- t is the time taken for the stone to reach the surface.
In this case, the stone takes 5 seconds to reach the surface, so we can substitute the values into the equation:
h = 1/2 * 9.8 * (5)^2
h = 1/2 * 9.8 * 25
h = 122.5 meters
Therefore, the depth of the well is 122.5 meters.
To calculate the velocity of the stone when it reaches the water's surface, we can use the equation for final velocity:
v = g * t
where:
- v is the final velocity,
- g is the acceleration due to gravity,
- t is the time taken for the stone to reach the surface.
By substituting the values into the equation:
v = 9.8 * 5
v = 49 m/s
Therefore, the velocity of the stone when it reaches the surface of the water is 49 m/s.