An aeroplane flies 400 m north and 300m south and then flies 1200 m upwards then net displacement is

Options

A. 1200 m
B. 1300 m
C. 1400 m
D. 1500 m

Explanation

To find the net displacement of the aeroplane, we will break down the motion into its components and apply the Pythagorean theorem. Here are the steps to solve the problem:

### Step 1: Analyze the Vertical and Horizontal Movements
The aeroplane moves:
- 400 m north
- 300 m south
- 1200 m upwards

### Step 2: Calculate the Net Displacement in the North-South Direction
The net displacement in the north-south direction can be calculated as follows:
- Displacement north = 400 m
- Displacement south = 300 m

Net displacement in the north-south direction:
\[ \text{Net displacement} = 400 \, \text{m (north)} - 300 \, \text{m (south)} = 100 \, \text{m (north)} \]

### Step 3: Identify the Vertical Displacement
The vertical displacement is given as:
\[ \text{Vertical displacement} = 1200 \, \text{m (upwards)} \]

### Step 4: Use the Pythagorean Theorem to Find the Resultant Displacement
Now, we can find the resultant displacement using the Pythagorean theorem. The net displacement forms a right triangle where:
- One leg is the net displacement in the north-south direction (100 m)
- The other leg is the vertical displacement (1200 m)

Using the Pythagorean theorem:
\[ \text{Resultant displacement} = \sqrt{(100 \, \text{m})^2 + (1200 \, \text{m})^2} \]
\[ = \sqrt{10000 + 1440000} \]
\[ = \sqrt{1450000} \]
\[ \approx 1204.16 \, \text{m} \]

### Step 5: Round the Result
Since the question does not specify the need for decimal precision, we can round the result:
\[ \text{Net displacement} \approx 1200 \, \text{m} \]

### Final Answer
The net displacement of the aeroplane is approximately **1200 m**.

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