An aeroplane moving horizontally with a speed of 180 km/hr drops a food packet while flying at height of 490 m. The horizontal range is

Options

A. 180 m
B. 980 m
C. 500 m
D. 670 m

Explanation

To solve the problem of finding the horizontal range of a food packet dropped from an airplane, we will follow these steps:

### Step 1: Convert the speed of the airplane from km/hr to m/s
The speed of the airplane is given as 180 km/hr. To convert this to meters per second (m/s), we use the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{5}{18} \]
Calculating this:
\[ \text{Speed in m/s} = 180 \times \frac{5}{18} = 50 \text{ m/s} \]

### Step 2: Calculate the time taken for the packet to fall to the ground
The height from which the packet is dropped is 490 m. We can use the formula for the time of free fall:
\[ t = \sqrt{\frac{2h}{g}} \]
Where:
- \( h = 490 \) m (height)
- \( g = 9.8 \) m/s² (acceleration due to gravity)

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 range
The horizontal range can be calculated using the formula:
\[ \text{Range} = \text{Horizontal Velocity} \times \text{Time} \]
Substituting the values we have:
\[ \text{Range} = 50 \text{ m/s} \times 10 \text{ s} = 500 \text{ m} \]

### Conclusion
The horizontal range of the food packet is 500 meters.

### Final Answer
The correct option is **500 meters**.

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