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 of finding the displacement of the car from its initial position, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion**:
The car moves in two segments:
- First, it travels 60 km/h for 1 hour towards the east.
- Then, it travels 60 km/h for 30 minutes (which is 0.5 hours) towards the south.

2. **Calculate the Distance Traveled East**:
- Speed = 60 km/h
- Time = 1 hour
- Distance (East) = Speed × Time = 60 km/h × 1 h = 60 km

3. **Calculate the Distance Traveled South**:
- Speed = 60 km/h
- Time = 30 minutes = 0.5 hours
- Distance (South) = Speed × Time = 60 km/h × 0.5 h = 30 km

4. **Visualize the Motion**:
- The car moves 60 km east and then 30 km south. This creates a right triangle where:
- One leg (base) = 60 km (east)
- Other leg (perpendicular) = 30 km (south)

5. **Use the Pythagorean Theorem to Find Displacement**:
- According to the Pythagorean theorem:
\[ h^2 = a^2 + b^2 \]
where \( h \) is the hypotenuse (displacement), \( a \) is the distance traveled east (60 km), and \( b \) is the distance traveled south (30 km).
- Substitute the values:
\[ h^2 = (60)^2 + (30)^2 \]
\[ h^2 = 3600 + 900 \]
\[ h^2 = 4500 \]
- Take the square root to find \( h \):
\[ h = \sqrt{4500} = 30\sqrt{5} \text{ km} \]

6. **Conclusion**:
The displacement of the car from its initial position is \( 30\sqrt{5} \) km.