A bus appears to go with a speed of 25 km/hr to a car driver, driving at the rate 7 km/hr northwards. If the bus actually travels in east direction, its speed is

Options

A. 24 km/h
B. 23 km/h
C. 26 km/h
D. 30 km/h

Answer

To solve the problem, we need to find the actual speed of the bus that is traveling eastward as perceived by a car driver moving northward. We will use the concept of relative velocity and the Pythagorean theorem.

### Step-by-Step Solution:

1. **Identify the velocities:**
- The speed of the car (V_car) = 7 km/hr (northward).
- The apparent speed of the bus (V_bus_apparent) = 25 km/hr (as seen by the car driver).

2. **Direction of motion:**
- The car is moving northward.
- The bus is moving eastward.

3. **Relative velocity concept:**
- The relative velocity of the bus with respect to the car can be calculated using the formula:
\[ V_{bus, relative} = \sqrt{V_{bus}^2 + V_{car}^2} \]
- Here, \( V_{bus, relative} \) is the apparent speed of the bus as seen by the car driver, which is given as 25 km/hr.

4. **Set up the equation:**
- We can rearrange the equation to find the actual speed of the bus (V_bus):
\[ V_{bus, relative}^2 = V_{bus}^2 + V_{car}^2 \]
- Substituting the known values:
\[ 25^2 = V_{bus}^2 + 7^2 \]

5. **Calculate the squares:**
- Calculate \( 25^2 \) and \( 7^2 \):
\[ 625 = V_{bus}^2 + 49 \]

6. **Rearranging the equation:**
- Now, isolate \( V_{bus}^2 \):
\[ V_{bus}^2 = 625 - 49 \]
\[ V_{bus}^2 = 576 \]

7. **Taking the square root:**
- Finally, take the square root to find \( V_{bus} \):
\[ V_{bus} = \sqrt{576} = 24 \text{ km/hr} \]

### Final Answer:
The actual speed of the bus is **24 km/hr**.

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