A ball is dropped downwards . After 1 second another ball is dropped downwards from the same point . What is the distance between them after 3 seconds .

Options

A. 20 m
B. 9.8m
C. 25 m
D. 50 m

Explanation

To solve the problem of finding the distance between two balls dropped from the same point, we can follow these steps:

### Step 1: Understand the Motion of the Balls
- The first ball is dropped and falls for 3 seconds.
- The second ball is dropped 1 second later, so it falls for 2 seconds.

### Step 2: Use the Equation of Motion
The distance fallen by an object in free fall can be calculated using the equation:
\[ s = ut + \frac{1}{2}gt^2 \]
where:
- \( s \) = distance fallen
- \( u \) = initial velocity (which is 0 for both balls)
- \( g \) = acceleration due to gravity (approximately \( 10 \, \text{m/s}^2 \))
- \( t \) = time in seconds

### Step 3: Calculate the Distance for the First Ball
For the first ball, which falls for 3 seconds:
- \( u = 0 \)
- \( g = 10 \, \text{m/s}^2 \)
- \( t = 3 \, \text{s} \)

Substituting the values into the equation:
\[ s_1 = 0 \cdot 3 + \frac{1}{2} \cdot 10 \cdot (3)^2 \]
\[ s_1 = 0 + \frac{1}{2} \cdot 10 \cdot 9 \]
\[ s_1 = 5 \cdot 9 = 45 \, \text{m} \]

### Step 4: Calculate the Distance for the Second Ball
For the second ball, which falls for 2 seconds:
- \( u = 0 \)
- \( g = 10 \, \text{m/s}^2 \)
- \( t = 2 \, \text{s} \)

Substituting the values into the equation:
\[ s_2 = 0 \cdot 2 + \frac{1}{2} \cdot 10 \cdot (2)^2 \]
\[ s_2 = 0 + \frac{1}{2} \cdot 10 \cdot 4 \]
\[ s_2 = 5 \cdot 4 = 20 \, \text{m} \]

### Step 5: Calculate the Distance Between the Two Balls
Now, we find the distance between the two balls after 3 seconds:
\[ \text{Distance} = s_1 - s_2 \]
\[ \text{Distance} = 45 \, \text{m} - 20 \, \text{m} = 25 \, \text{m} \]

### Final Answer
The distance between the two balls after 3 seconds is **25 meters**.

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