An aeroplane takes off at an angle of `30^@` to the horizontal. If the velocity of the plane is 200 Km/hr, then the vertical component of its velocity is 100% (in Km/hr). Find the value of x.

Explanation

To find the value of \( x \) in the given problem, we need to calculate the vertical component of the velocity of the airplane taking off at an angle of \( 30^\circ \) with a speed of \( 200 \, \text{km/hr} \).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Velocity of the airplane, \( V = 200 \, \text{km/hr} \)
- Angle of takeoff, \( \theta = 30^\circ \)

2. **Understand the Components of Velocity**:
- The velocity can be broken down into two components: horizontal and vertical.
- The vertical component of the velocity (\( V_y \)) can be calculated using the sine function:
\[ V_y = V \sin(\theta) \]

3. **Calculate the Vertical Component**:
- Substitute the known values into the equation:
\[ V_y = 200 \sin(30^\circ) \]
- We know that \( \sin(30^\circ) = \frac{1}{2} \):
\[ V_y = 200 \times \frac{1}{2} = 100 \, \text{km/hr} \]

4. **Relate the Vertical Component to the Given Expression**:
- According to the problem, the vertical component of the velocity is given as \( 100x \, \text{km/hr} \).
- We have calculated \( V_y = 100 \, \text{km/hr} \).
- Therefore, we can set up the equation:
\[ 100x = 100 \]

5. **Solve for \( x \)**:
- Divide both sides by 100:
\[ x = 1 \]

### Final Answer:
The value of \( x \) is \( 1 \).

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