A man of `50 kg` mass is standing in a gravity free space at a height of `10m` above the floor. He throws a stone of `0.5 kg` mass downwards with a speed `2m//s`. When the stone reaches the floor, the distance of the man above the floor will be

Options

A. `9.9 m`
B. `10.1 m`
C. `1.0 m`
D. `20 m`

Explanation

To solve the problem, we need to analyze the situation step by step.

### Step 1: Understand the scenario
A man with a mass of 50 kg is standing at a height of 10 meters above the floor in a gravity-free space. He throws a stone of mass 0.5 kg downwards with an initial speed of 2 m/s.

### Step 2: Determine the time taken for the stone to reach the floor
Since the man is in gravity-free space, we can assume that there is no gravitational force acting on the stone after it is thrown. The stone will continue to move downwards with the initial velocity it was thrown with.

The distance the stone needs to cover to reach the floor is 10 meters. The stone is thrown downwards with an initial speed of 2 m/s.

Using the formula for distance:
\[ \text{Distance} = \text{Initial Velocity} \times \text{Time} \]
We can rearrange this to find time:
\[ \text{Time} = \frac{\text{Distance}}{\text{Initial Velocity}} \]
Substituting the values:
\[ \text{Time} = \frac{10 \, \text{m}}{2 \, \text{m/s}} = 5 \, \text{s} \]

### Step 3: Determine the distance the man moves during this time
In gravity-free space, the man will not move upwards or downwards due to the absence of any gravitational force acting on him. Therefore, he will remain at the same height above the floor.

### Step 4: Calculate the man's height above the floor when the stone reaches the floor
Since the man does not move, he will still be at the height of 10 meters above the floor when the stone reaches the floor.

### Final Answer
The distance of the man above the floor when the stone reaches the floor will be **10 meters**.

---