Two balls are dropped simultaneously from two points separated by a vertical height of 6 m. The distance of separation between them after next 2s is

Options

A. 9.8 m
B. 6 m
C. 12 m
D. 0

Answer

To solve the problem, we need to analyze the motion of the two balls dropped from different heights. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Problem
We have two balls dropped from two different heights, separated by a vertical distance of 6 meters. We need to find the distance of separation between them after 2 seconds.

### Step 2: Identify Initial Conditions
Both balls are dropped simultaneously, which means:
- Initial velocity of both balls (u₁ and u₂) = 0 m/s (since they are dropped)
- The acceleration due to gravity (g) = 9.81 m/s² (approximately 10 m/s² for simplicity)

### Step 3: Calculate the Distance Fallen by Each Ball
Using the equation of motion for distance fallen under gravity:
\[ s = ut + \frac{1}{2} g t^2 \]
Since both balls are dropped from rest (u = 0), the equation simplifies to:
\[ s = \frac{1}{2} g t^2 \]

### Step 4: Calculate Distance Fallen After 2 Seconds
Substituting g = 10 m/s² and t = 2 s into the equation:
\[ s = \frac{1}{2} \times 10 \times (2)^2 \]
\[ s = \frac{1}{2} \times 10 \times 4 \]
\[ s = 20 \text{ meters} \]

### Step 5: Analyze the Separation After 2 Seconds
Since both balls are dropped from rest and have the same acceleration due to gravity, they will fall the same distance in the same time. Therefore, the distance fallen by both balls after 2 seconds is the same.

### Step 6: Determine the New Distance of Separation
Initially, the distance of separation between the two balls was 6 meters. After 2 seconds, since both balls have fallen the same distance, the separation remains unchanged.

Thus, the distance of separation after 2 seconds is still:
\[ \text{Distance of separation} = 6 \text{ meters} \]

### Final Answer
The distance of separation between the two balls after the next 2 seconds is **6 meters**.

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