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A train A is moving towards east with a...

A train A is moving towards east with a velocity of 30 km/h and another train B is moving on parallel lines towards west with a speed of 40 km/ h . The velocity of train A relative to train B is

A

10 km/h

B

70 km/h tosards east

C

70 km/h towards west

D

none of these

Text Solution

AI Generated Solution

The correct Answer is:
To find the velocity of train A relative to train B, we can use the concept of relative velocity. The relative velocity of one object with respect to another is calculated by subtracting the velocity of the second object from the velocity of the first object. **Step 1: Identify the velocities of the trains.** - Velocity of train A (V_A) = 30 km/h (towards east) - Velocity of train B (V_B) = 40 km/h (towards west) **Step 2: Assign directions to the velocities.** - We can consider east as the positive direction and west as the negative direction. - Therefore, we can express the velocities as: - V_A = +30 km/h (east) - V_B = -40 km/h (west) **Step 3: Calculate the relative velocity of train A with respect to train B.** The formula for relative velocity (V_AB) is given by: \[ V_{AB} = V_A - V_B \] Substituting the values we have: \[ V_{AB} = 30 \text{ km/h} - (-40 \text{ km/h}) \] \[ V_{AB} = 30 \text{ km/h} + 40 \text{ km/h} \] \[ V_{AB} = 70 \text{ km/h} \] **Step 4: Determine the direction of the relative velocity.** Since train A is moving towards the east and train B is moving towards the west, the relative velocity of train A with respect to train B is towards the east. **Final Answer:** The velocity of train A relative to train B is 70 km/h towards the east. ---
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