A a certain instant of time a ballon is moving downwards with speed of 5m/s. It has a constant retardation of 5m/s2. A man in the ballon drops a stone at that instant. It hits the ground after 2s. Then the speed with which the stone hits the ground is.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the initial conditions
The balloon is moving downwards with a speed of 5 m/s. This means that the initial velocity of the stone when it is dropped is also 5 m/s downwards.

### Step 2: Identify the acceleration
The balloon has a constant retardation (deceleration) of 5 m/s². This means that the acceleration of the balloon is -5 m/s² (upwards). However, once the stone is dropped, it will only experience the acceleration due to gravity, which is approximately -10 m/s² (downwards).

### Step 3: Set up the equation for the stone's motion
When the stone is dropped, its initial velocity (u) is -5 m/s (downwards), and it will accelerate downwards due to gravity at -10 m/s². We need to find the final velocity (v) of the stone after it falls for 2 seconds (t = 2 s).

### Step 4: Apply the kinematic equation
We will use the kinematic equation:
\[ v = u + at \]
Where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

### Step 5: Substitute the values into the equation
Here, \( u = -5 \, \text{m/s} \), \( a = -10 \, \text{m/s}^2 \), and \( t = 2 \, \text{s} \).

Substituting these values into the equation:
\[ v = -5 + (-10) \times 2 \]
\[ v = -5 - 20 \]
\[ v = -25 \, \text{m/s} \]

### Step 6: Interpret the result
The negative sign indicates that the stone is moving downwards. Therefore, the speed with which the stone hits the ground is 25 m/s.

### Final Answer
The speed with which the stone hits the ground is **25 m/s**.

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