A car moves with speed `60 km//h` for 1 hour in east direction and with same speed for 30 min in south direction. The displacement of car from initial posilion is

Options

A. 60 km
B. `30sqrt(3) km`
C. `30sqrt(5) km`
D. `60sqrt(2) km`

Answer

To solve the problem step by step, we will calculate the displacement of the car from its initial position after it has moved in two different directions.

### Step 1: Calculate the distance traveled in the east direction.
The car moves with a speed of 60 km/h for 1 hour in the east direction.

\[ \text{Distance}_{\text{east}} = \text{Speed} \times \text{Time} = 60 \, \text{km/h} \times 1 \, \text{h} = 60 \, \text{km} \]

### Step 2: Calculate the distance traveled in the south direction.
The car then moves with the same speed for 30 minutes (which is 0.5 hours) in the south direction.

\[ \text{Distance}_{\text{south}} = \text{Speed} \times \text{Time} = 60 \, \text{km/h} \times 0.5 \, \text{h} = 30 \, \text{km} \]

### Step 3: Visualize the movement.
The car's movement can be visualized as forming a right triangle where:
- One leg (east direction) is 60 km.
- The other leg (south direction) is 30 km.

### Step 4: Apply the Pythagorean theorem to find the displacement.
To find the displacement (d), we use the Pythagorean theorem, which states:

\[ d^2 = (\text{Distance}_{\text{east}})^2 + (\text{Distance}_{\text{south}})^2 \]

Substituting the values:

\[ d^2 = (60 \, \text{km})^2 + (30 \, \text{km})^2 \]

Calculating the squares:

\[ d^2 = 3600 \, \text{km}^2 + 900 \, \text{km}^2 = 4500 \, \text{km}^2 \]

### Step 5: Calculate the displacement.
Taking the square root to find d:

\[ d = \sqrt{4500 \, \text{km}^2} = \sqrt{4500} \, \text{km} \]

This can be simplified:

\[ d = \sqrt{100 \times 45} = 10 \sqrt{45} \, \text{km} = 30 \sqrt{5} \, \text{km} \]

### Final Answer:
The displacement of the car from its initial position is:

\[ d = 30 \sqrt{5} \, \text{km} \]