Question

Train A is moving along two parallel rail tracks towards north with speed 72 km/h and train B is moving towards south with speed 108 km/h.Velocity of train B with respect to A and velocity of ground with respect to B are (in m/s) :

• A. –30 and 50
• B. –50 and –30
• C. –50 and 30
• D. 50 and –30

Answer 1

Answer: (C)

–50 and 30

Answer 2

Given: - Speed of train A: $v_A = 72 \, \text{km/h}$ - Speed of train B: $v_B = 108 \, \text{km/h}$

Step 1: Converting Speeds to SI Units

To convert the speeds from km/h to m/s:

$v_A = 72 \times \frac{1000}{3600} = 20 \, \text{m/s}$ $v_B = 108 \times \frac{1000}{3600} = 30 \, \text{m/s}$

Step 2: Calculating the Velocity of B with Respect to A

The relative velocity of train $B$ with respect to train $A$ is given by:

$v_{BA} = v_B - (-v_A) = v_B + v_A$

Substituting the values:

$v_{BA} = 30 + 20 = 50 \, \text{m/s}$

Since train $B$ is moving towards the south and train $A$ is moving towards the north, the relative velocity is considered negative:

$v_{BA} = -50 \, \text{m/s}$

Step 3: Calculating the Velocity of the Ground with Respect to B

The velocity of the ground with respect to train $B$ is simply the negative of the velocity of train $B$ with respect to the ground:

$v_{\text{ground with respect to } B} = -v_B = -30 \, \text{m/s}$

Conclusion:

The velocity of train $B$ with respect to $A$ is $-50 \, \text{m/s}$ and the velocity of the ground with respect to $B$ is $-30 \, \text{m/s}$.