An aeroplane flying 490 m above the ground level at 100 m/s, releases a block. How far on the ground will it strike-

Options

A. `0.1 km`
B. `1 km`
C. `2 km `
D. none of the above

Answer

To solve the problem of how far on the ground the block will strike after being released from the aeroplane, we can break the solution down into several clear steps.

### Step 1: Identify the given values
- Height (h) = 490 m
- Speed of the airplane (v) = 100 m/s
- Acceleration due to gravity (g) = 9.8 m/s²

### Step 2: Calculate the time taken for the block to fall
The time (t) taken for the block to fall from the height can be calculated using the formula for free fall:
\[ t = \sqrt{\frac{2h}{g}} \]
Substituting the values:
\[ t = \sqrt{\frac{2 \times 490}{9.8}} = \sqrt{\frac{980}{9.8}} = \sqrt{100} = 10 \text{ seconds} \]

### Step 3: Calculate the horizontal distance traveled by the block
The horizontal distance (d) traveled by the block while it falls can be calculated using the formula:
\[ d = v \times t \]
Substituting the values:
\[ d = 100 \text{ m/s} \times 10 \text{ s} = 1000 \text{ m} \]

### Step 4: Conclusion
The block will strike the ground at a distance of 1000 meters from the point directly below where it was released.

### Final Answer
The block will strike the ground 1000 meters away from the point of release.

---