From a ballon rising vertically upwards at 5 m/s, a stone is thrown up at 10 m/s relative to the balloon. Its velocity with respect to ground after 2 sec is - (assume g = 10 `m//s^(2)`)

Options

A. 0
B. 20 m/s
C. 10 m/s
D. 5 m/s

Explanation

To solve the problem, we need to determine the velocity of the stone with respect to the ground after 2 seconds. We will break down the solution into clear steps.

### Step-by-Step Solution:

1. **Identify the velocities:**
- The balloon is rising vertically upwards with a velocity of \( V_b = 5 \, \text{m/s} \).
- The stone is thrown upwards with a velocity of \( V_{s/b} = 10 \, \text{m/s} \) relative to the balloon.

2. **Calculate the initial velocity of the stone with respect to the ground:**
- Since both the balloon and the stone are moving in the same direction (upwards), we can find the stone's velocity with respect to the ground using the formula:
\[ V_s = V_{s/b} + V_b \]
- Substituting the values:
\[ V_s = 10 \, \text{m/s} + 5 \, \text{m/s} = 15 \, \text{m/s} \]

3. **Use the kinematic equation to find the velocity after 2 seconds:**
- We will use the equation:
\[ V = U + a t \]
- Here, \( U \) is the initial velocity of the stone, \( a \) is the acceleration due to gravity (which acts downwards, hence it is negative), and \( t \) is the time.
- Given \( U = 15 \, \text{m/s} \), \( a = -10 \, \text{m/s}^2 \), and \( t = 2 \, \text{s} \):
\[ V = 15 \, \text{m/s} + (-10 \, \text{m/s}^2)(2 \, \text{s}) \]
- Calculating this gives:
\[ V = 15 \, \text{m/s} - 20 \, \text{m/s} = -5 \, \text{m/s} \]

4. **Conclusion:**
- The velocity of the stone with respect to the ground after 2 seconds is \( -5 \, \text{m/s} \). The negative sign indicates that the stone is moving downwards.

### Final Answer:
The velocity of the stone with respect to the ground after 2 seconds is \( -5 \, \text{m/s} \).