balloon is rising vertically up with a velocity of 29 m/s. A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it is `(g = 9.8 m/s^2)`

Options

A. 100m
B. 200m
C. 400m
D. 150m

Answer

To solve the problem, we need to find the height of the balloon when the stone was dropped from it. We will use the second equation of motion to do this.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Initial velocity of the stone (u) = 29 m/s (upward, same as the balloon's velocity)
- Time taken to reach the ground (t) = 10 s
- Acceleration due to gravity (g) = 9.8 m/s² (downward, so we will take it as -9.8 m/s²)

2. **Use the Second Equation of Motion:**
The second equation of motion is given by:
\[ h = ut + \frac{1}{2} a t^2 \]
Here, \(a\) is the acceleration, which will be -g (since it acts downward).

3. **Substituting the Values:**
- Substitute \(u = 29\) m/s, \(t = 10\) s, and \(a = -9.8\) m/s² into the equation:
\[ h = (29 \, \text{m/s}) \times (10 \, \text{s}) + \frac{1}{2} \times (-9.8 \, \text{m/s}^2) \times (10 \, \text{s})^2 \]

4. **Calculating Each Term:**
- First term: \(29 \times 10 = 290\) m
- Second term:
\[ \frac{1}{2} \times (-9.8) \times 100 = -490 \, \text{m} \]

5. **Combining the Results:**
\[ h = 290 - 490 = -200 \, \text{m} \]

6. **Interpreting the Result:**
Since we are looking for height, we take the absolute value:
\[ h = 200 \, \text{m} \]

### Final Answer:
The height of the balloon when the stone was dropped from it is **200 meters**.