Two balls are dropped from the same point after an interval of 1s. If acceleration due to gravity is `10 m//s^(2)`, what will be their separation 3 seconds after the release of first ball?

Options

A. 5 m
B. 10 m
C. 25 m
D. 30 m

Answer

To solve the problem, we need to find the positions of both balls after 3 seconds and then calculate their separation.

### Step 1: Determine the position of the first ball after 3 seconds.

The first ball is dropped from rest, so its initial velocity (u) is 0. The formula for the distance (s) covered under constant acceleration is given by:

\[ s = ut + \frac{1}{2} a t^2 \]

Where:
- \( u = 0 \) (initial velocity)
- \( a = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( t = 3 \, \text{s} \) (time)

Substituting the values:

\[ s_1 = 0 \cdot 3 + \frac{1}{2} \cdot 10 \cdot (3)^2 \]

Calculating this gives:

\[ s_1 = 0 + \frac{1}{2} \cdot 10 \cdot 9 = 45 \, \text{m} \]

So, the position of the first ball after 3 seconds is \( 45 \, \text{m} \).

### Step 2: Determine the position of the second ball after 2 seconds.

The second ball is dropped 1 second after the first ball, so it has been falling for only 2 seconds when we measure the separation at 3 seconds.

Using the same formula for the second ball:

\[ s_2 = u t + \frac{1}{2} a t^2 \]

Where:
- \( u = 0 \) (initial velocity)
- \( a = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( t = 2 \, \text{s} \) (time since it was dropped)

Substituting the values:

\[ s_2 = 0 \cdot 2 + \frac{1}{2} \cdot 10 \cdot (2)^2 \]

Calculating this gives:

\[ s_2 = 0 + \frac{1}{2} \cdot 10 \cdot 4 = 20 \, \text{m} \]

So, the position of the second ball after 2 seconds is \( 20 \, \text{m} \).

### Step 3: Calculate the separation between the two balls.

Now, we can find the separation between the two balls after 3 seconds:

\[ \text{Separation} = s_1 - s_2 = 45 \, \text{m} - 20 \, \text{m} = 25 \, \text{m} \]

### Final Answer

The separation between the two balls 3 seconds after the release of the first ball is \( 25 \, \text{m} \).

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