A food packed is dropped, from a height of 500 m, from a plane flying horizontally with speed 100km/h. The packet reaches to the ground after travelling a horizontal distance. [ Take g ` = 10 ms^(-2)`]

Options

A. 100m
B. 204.5 m
C. 500 m
D. 277. 7 m

Answer

To solve the problem of finding the horizontal distance traveled by a food packet dropped from a height of 500 m from a plane flying horizontally at a speed of 100 km/h, we can follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed of the plane is given as 100 km/h. We need to convert this speed into meters per second (m/s) for our calculations.

\[ \text{Speed in m/s} = \frac{100 \times 1000}{3600} = \frac{100000}{3600} \approx 27.78 \, \text{m/s} \]

### Step 2: Calculate the time taken to fall 500 m
We will use the equation of motion to find the time taken for the packet to fall from a height of 500 m. The formula we will use is:

\[ s = ut + \frac{1}{2} a t^2 \]

Where:
- \(s\) = vertical distance (500 m)
- \(u\) = initial vertical velocity (0 m/s, since it is dropped)
- \(a\) = acceleration due to gravity (10 m/s²)
- \(t\) = time in seconds

Substituting the values:

\[ 500 = 0 \cdot t + \frac{1}{2} \cdot 10 \cdot t^2 \]

This simplifies to:

\[ 500 = 5t^2 \]

Now, solving for \(t^2\):

\[ t^2 = \frac{500}{5} = 100 \]

Taking the square root:

\[ t = \sqrt{100} = 10 \, \text{s} \]

### Step 3: Calculate the horizontal distance traveled
Now that we have the time of flight, we can calculate the horizontal distance traveled using the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the values:

\[ \text{Distance} = 27.78 \, \text{m/s} \times 10 \, \text{s} = 277.8 \, \text{m} \]

### Final Answer
The horizontal distance traveled by the food packet is approximately **277.8 meters**.

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