Certainly! Let's find the height of the building step-by-step based on the given information:
1. Understanding the problem:
- A student drops a stone from the top of the building.
- The student starts a clock at the moment the stone is dropped.
- The student stops the clock as soon as the stone hits the ground.
- We need to determine the height (\(h\)) of the building using the relation \( h = \frac{1}{2} g t^2 \).
2. Given data:
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
- Time taken for the stone to hit the ground, \( t = 3 \, \text{seconds} \)
3. Using the relation \( h = \frac{1}{2} g t^2 \):
- Here, \( g = 9.8 \, \text{m/s}^2 \)
- \( t = 3 \, \text{seconds} \)
4. Substitute the values into the formula:
[tex]\[
h = \frac{1}{2} \times 9.8 \, \text{m/s}^2 \times (3 \, \text{seconds})^2
\][/tex]
5. Calculate the height:
- First, calculate \( t^2 \):
[tex]\[
t^2 = (3 \, \text{seconds})^2 = 9 \, \text{seconds}^2
\][/tex]
- Next, multiply \( g \) by this value and then by \(\frac{1}{2}\):
[tex]\[
h = \frac{1}{2} \times 9.8 \, \text{m/s}^2 \times 9 \, \text{seconds}^2
\][/tex]
[tex]\[
h = \frac{1}{2} \times 88.2 \, \text{m}
\][/tex]
[tex]\[
h = 44.1 \, \text{m}
\][/tex]
6. Final Answer:
- The height of the building is [tex]\( 44.1 \, \text{m} \)[/tex].
