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. 510m
C. 610 m
D. 725m

Answer

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 1: Identify the initial conditions
- The balloon is descending at a uniform rate of 12 m/s. This means that when the stone is released, it has an initial velocity (u) of -12 m/s (negative because it's moving downward).
- The acceleration (a) acting on the stone after it is released is due to gravity, which is approximately 9.8 m/s² downward.

### Step 2: Write the displacement formula
We will use the formula for displacement when acceleration is constant:
\[ s = ut + \frac{1}{2} a t^2 \]
where:
- \( s \) is the displacement,
- \( u \) is the initial velocity,
- \( a \) is the acceleration,
- \( t \) is the time.

### Step 3: Substitute the known values
Given:
- \( u = -12 \, \text{m/s} \)
- \( a = 9.8 \, \text{m/s}^2 \)
- \( t = 10 \, \text{s} \)

Now, substituting these values into the displacement formula:
\[ s = (-12)(10) + \frac{1}{2}(9.8)(10^2) \]

### Step 4: Calculate the displacement
Calculating each term:
1. The first term:
\[ -12 \times 10 = -120 \, \text{m} \]
2. The second term:
\[ \frac{1}{2} \times 9.8 \times 100 = 490 \, \text{m} \]

Now, combining both terms:
\[ s = -120 + 490 = 370 \, \text{m} \]

### Step 5: Conclusion
The displacement of the stone from the point of release after 10 seconds is **370 meters downward**.

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