Two stones are thrown from the same point with velocity of 5 `ms^(-1)` one vertically upwards and the other vertically downwards. When the first stone is at the highest point the relative velocity of the second stone with respect to the first stone is,

Options

A. `5ms^(-1)`
B. `0ms^(-1)`
C. `10ms^(-1)`
D. `-5ms^(-1)`

Explanation

To solve the problem, we need to determine the relative velocity of the second stone (thrown downwards) with respect to the first stone (thrown upwards) when the first stone reaches its highest point.

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- The first stone (Stone A) is thrown upwards with an initial velocity \( u_A = 5 \, \text{ms}^{-1} \).
- The second stone (Stone B) is thrown downwards with an initial velocity \( u_B = -5 \, \text{ms}^{-1} \) (negative because it is in the downward direction).

2. **Determine the Time Taken for Stone A to Reach the Highest Point**:
- At the highest point, the final velocity \( v_A = 0 \).
- We can use the equation of motion:
\[ v_A = u_A + a_A t \]
where \( a_A = -10 \, \text{ms}^{-2} \) (acceleration due to gravity acting downwards).
- Substituting the values:
\[ 0 = 5 - 10t \]
Rearranging gives:
\[ 10t = 5 \implies t = \frac{5}{10} = 0.5 \, \text{s} \]

3. **Calculate the Velocity of Stone B at \( t = 0.5 \, \text{s} \)**:
- We use the same equation of motion for Stone B:
\[ v_B = u_B + a_B t \]
where \( a_B = -10 \, \text{ms}^{-2} \).
- Substituting the values:
\[ v_B = -5 - 10(0.5) \]
\[ v_B = -5 - 5 = -10 \, \text{ms}^{-1} \]

4. **Determine the Relative Velocity**:
- The relative velocity of Stone B with respect to Stone A is given by:
\[ v_{BA} = v_B - v_A \]
- Since \( v_A = 0 \) at the highest point:
\[ v_{BA} = -10 - 0 = -10 \, \text{ms}^{-1} \]
- The magnitude of the relative velocity is \( 10 \, \text{ms}^{-1} \).

5. **Conclusion**:
- The relative velocity of the second stone with respect to the first stone when the first stone is at the highest point is \( 10 \, \text{ms}^{-1} \).

### Final Answer:
The relative velocity of the second stone with respect to the first stone is \( 10 \, \text{ms}^{-1} \).