Two cars start at the same time from one point and move along two roads at right angles to each other. Their speeds are 36 km/hr and 48 km/hr respectively. After 15 seconds, the distance between them will be

Options

A. 400 m
B. 150 m
C. 300 m
D. 250 m

Answer

To solve the problem step by step, we will calculate the distance traveled by each car in 15 seconds and then use the Pythagorean theorem to find the distance between them.

### Step 1: Convert the speeds from km/hr to m/s
To convert the speeds from kilometers per hour (km/hr) to meters per second (m/s), we use the conversion factor:
\[ \text{Speed in m/s} = \text{Speed in km/hr} \times \frac{5}{18} \]

For the first car:
\[ \text{Speed} = 36 \text{ km/hr} \]
\[ \text{Speed in m/s} = 36 \times \frac{5}{18} = 10 \text{ m/s} \]

For the second car:
\[ \text{Speed} = 48 \text{ km/hr} \]
\[ \text{Speed in m/s} = 48 \times \frac{5}{18} = 13.33 \text{ m/s} \]

### Step 2: Calculate the distance traveled by each car in 15 seconds
Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

For the first car:
\[ \text{Distance}_{A} = 10 \text{ m/s} \times 15 \text{ s} = 150 \text{ m} \]

For the second car:
\[ \text{Distance}_{B} = 13.33 \text{ m/s} \times 15 \text{ s} = 200 \text{ m} \]

### Step 3: Use the Pythagorean theorem to find the distance between the two cars
Since the two cars are moving at right angles to each other, we can use the Pythagorean theorem:
\[ \text{Distance} = \sqrt{(\text{Distance}_{A})^2 + (\text{Distance}_{B})^2} \]

Substituting the distances:
\[ \text{Distance} = \sqrt{(150)^2 + (200)^2} \]
\[ = \sqrt{22500 + 40000} \]
\[ = \sqrt{62500} \]
\[ = 250 \text{ m} \]

### Conclusion
The distance between the two cars after 15 seconds is **250 meters**.

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