A stone is dropped into a well and hits the water in 3.95 sec.  How deep is the well?  Record the magnitude of the rocks displacemenet downward.

To calculate the depth of the well, we can use the equations of motion under gravity. Since the stone is dropped (starting velocity \( u = 0 \)) and falls freely under gravity, we can use the following kinematic equation:

\[
d = ut + \frac{1}{2} g t^2
\]

Where:
- \( d \) is the depth (displacement) of the well,
- \( u = 0 \) m/s (initial velocity since it was dropped),
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity),
- \( t = 3.95 \, \text{seconds} \) (time it took to hit the water).

Substituting the values:

\[
d = 0 \times 3.95 + \frac{1}{2} \times 9.8 \times (3.95)^2
\]

Now, let’s compute the value of \( d \).The depth of the well is approximately 76.45 meters. This is the magnitude of the stone's displacement downward.

Do you have any questions or would you like further details?

Here are five related questions to expand on this topic:
1. How would the result change if the well were on the Moon, where gravity is weaker?
2. What if the stone had an initial velocity downward instead of being dropped?
3. How long would it take the stone to hit the water if the well were twice as deep?
4. How does air resistance affect the motion of the stone in real life?
5. Can you derive the formula for displacement from the basic laws of motion?

**Tip**: Always keep track of units when solving physics problems to avoid mistakes!

A stone is dropped into a well and hits the water in 3.95 sec. How deep is the well? Record the magnitude of the rock's displacement downward.

Discover how to calculate the depth of a well using the kinematic equations of motion. Learn to apply the formula d = (1/2) * g * t^2 for a stone dropped from rest, determining the well's depth in meters. Suitable for high school students in Grades 9-12.

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