An aeroplane is flying in a horizontal direction with a velocity `600 km//h` at a height of 1960 m. When it is vertically above the point A on the ground, a body is dropped from it. The body strikes the ground at point B. Calculate the distance AB.

Explanation

To solve the problem of finding the distance \( AB \) where a body dropped from an airplane strikes the ground, we can break the solution into the following steps:

### Step 1: Understand the Problem
The airplane is flying horizontally at a height of 1960 m with a velocity of 600 km/h. When the body is dropped, it will fall vertically under the influence of gravity while also moving horizontally due to the airplane's velocity.

### Step 2: Convert the Velocity
Convert the velocity of the airplane from km/h to m/s:
\[ 600 \text{ km/h} = \frac{600 \times 1000 \text{ m}}{3600 \text{ s}} = \frac{600000}{3600} = 166.67 \text{ m/s} \]

### Step 3: Calculate the Time of Fall
Using the equation of motion for vertical motion:
\[ s = ut + \frac{1}{2} a t^2 \]
where:
- \( s = 1960 \) m (the height from which the body is dropped),
- \( u = 0 \) m/s (initial vertical velocity),
- \( a = -9.8 \) m/s² (acceleration due to gravity).

Substituting the values:
\[ 1960 = 0 \cdot t + \frac{1}{2} \cdot (-9.8) \cdot t^2 \]
This simplifies to:
\[ 1960 = -4.9 t^2 \]
Rearranging gives:
\[ t^2 = \frac{1960}{4.9} \approx 400 \]
Taking the square root:
\[ t = \sqrt{400} = 20 \text{ seconds} \]

### Step 4: Calculate the Horizontal Distance
Now, using the horizontal motion to find the distance \( AB \):
\[ d = vt \]
where:
- \( v = 166.67 \) m/s (horizontal velocity),
- \( t = 20 \) s (time of fall).

Substituting the values:
\[ d = 166.67 \cdot 20 = 3333.33 \text{ m} \]

### Step 5: Conclusion
The distance \( AB \) where the body strikes the ground is approximately:
\[ AB \approx 3333.33 \text{ m} \]