A stone falls from a ballon that id descending at a uniform rate of 12m/s. The displacement of the stone from the point of release after 10 sec is

Options

A. `490 m`
B. ` 510 m `
C. ` 610 m `
D. `725 m `

Explanation

To solve the problem of a stone falling from a balloon that is descending at a uniform rate of 12 m/s, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Conditions:**
- The balloon is descending at a uniform rate of 12 m/s, which means the initial velocity (u) of the stone when it is released is -12 m/s (negative because it is moving downward).
- The acceleration (a) acting on the stone due to gravity is -9.8 m/s² (also negative since it is directed downward).
- The time (t) for which the stone falls is 10 seconds.

2. **Use the Second Equation of Motion:**
The second equation of motion is given by:
\[ s = ut + \frac{1}{2} a t^2 \]
where:
- \( s \) is the displacement,
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time.

3. **Substitute the Values:**
Substitute the known values into the equation:
\[ s = (-12 \, \text{m/s}) \times (10 \, \text{s}) + \frac{1}{2} \times (-9.8 \, \text{m/s}^2) \times (10 \, \text{s})^2 \]

4. **Calculate Each Term:**
- First term:
\[ -12 \times 10 = -120 \, \text{m} \]
- Second term:
\[ \frac{1}{2} \times (-9.8) \times (100) = -490 \, \text{m} \]

5. **Combine the Terms:**
Now, combine both terms:
\[ s = -120 \, \text{m} - 490 \, \text{m} = -610 \, \text{m} \]

6. **Interpret the Result:**
The negative sign indicates the direction of displacement is downward. Therefore, the magnitude of the displacement from the point of release after 10 seconds is:
\[ |s| = 610 \, \text{m} \]

### Final Answer:
The displacement of the stone from the point of release after 10 seconds is 610 meters downward.

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