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. zero
B. `5 ms ^(-1)`
C. `10 ms ^(-1)`
D. `20 ms ^(-1)`

Answer

To solve the problem step by step, we will break down the motion of the stone thrown from the balloon and calculate its velocity with respect to the ground after 2 seconds.

### Step 1: Identify the initial velocities
The balloon is rising vertically upwards at a speed of 5 m/s. The stone is thrown upwards at a speed of 10 m/s relative to the balloon.

**Initial velocity of the stone with respect to the ground (u):**
- Velocity of the balloon (upwards) = 5 m/s
- Velocity of the stone relative to the balloon (upwards) = 10 m/s

Thus, the initial velocity of the stone with respect to the ground is:
\[ u = \text{Velocity of balloon} + \text{Velocity of stone relative to balloon} \]
\[ u = 5 \, \text{m/s} + 10 \, \text{m/s} = 15 \, \text{m/s} \]

### Step 2: Calculate the final velocity after 2 seconds
To find the final velocity of the stone after 2 seconds, we will use the equation of motion:
\[ v = u - g \cdot t \]
Where:
- \( v \) = final velocity
- \( u \) = initial velocity (15 m/s)
- \( g \) = acceleration due to gravity (10 m/s²)
- \( t \) = time (2 seconds)

Substituting the values into the equation:
\[ v = 15 \, \text{m/s} - (10 \, \text{m/s}^2 \cdot 2 \, \text{s}) \]
\[ v = 15 \, \text{m/s} - 20 \, \text{m/s} \]
\[ v = -5 \, \text{m/s} \]

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

---