An airplane is flying horizontally at a height of 490m with a velocity of `150ms^(-1)`. A bag containing food is to be dropped to the Jawans on the ground. How far (in meter) from them should the bag the dropped so that it directely reaches them?

Explanation

To solve the problem of how far from the Jawans the bag should be dropped so that it directly reaches them, we can follow these steps:

### Step 1: Determine the time taken for the bag to fall
The bag is dropped from a height of 490 meters. We can use the equation of motion for free fall to find the time taken for the bag to reach the ground:

\[ S = ut + \frac{1}{2}gt^2 \]

Where:
- \( S \) is the distance fallen (490 m)
- \( u \) is the initial velocity (0 m/s, since the bag is dropped)
- \( g \) is the acceleration due to gravity (approximately \( 10 \, m/s^2 \))
- \( t \) is the time in seconds

Substituting the known values:

\[ 490 = 0 \cdot t + \frac{1}{2} \cdot 10 \cdot t^2 \]

This simplifies to:

\[ 490 = 5t^2 \]

### Step 2: Solve for \( t^2 \)
Rearranging the equation gives us:

\[ t^2 = \frac{490}{5} = 98 \]

Taking the square root:

\[ t = \sqrt{98} \approx 9.9 \, \text{s} \]

### Step 3: Calculate the horizontal distance
Now that we have the time it takes for the bag to fall, we can calculate how far the airplane travels horizontally during this time. The horizontal distance \( d \) can be calculated using the formula:

\[ d = vt \]

Where:
- \( v \) is the horizontal velocity of the airplane (150 m/s)
- \( t \) is the time calculated in the previous step (approximately 9.9 s)

Substituting the values:

\[ d = 150 \cdot 9.9 \approx 1485 \, \text{m} \]

### Step 4: Conclusion
Thus, the bag should be dropped approximately **1485 meters** away from the Jawans to ensure it lands directly on them.

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