Two parallel rail tracks run north-south. On one track train A moves north with a speed of 54 km h-1 and on the other track train B moves south with a speed of 90 km h-1 . The velocity of train A with respect to train B is

Question

Two parallel rail tracks run north-south. On one track train A moves north with a speed of 54 km h-1 and on the other track train B moves south with a speed of 90 km h-1 . The velocity of train A with respect to train B is (A)  10 ms-1  (B)  15 ms-1  (C)  25 ms-1  (D)  40 ms-1

Tardigrade Admin · Accepted Answer

Let the positive direction of motion be from south to north.
Velocity of train

A

with respect to ground

v_{A G} = + 54 km h^{- 1} = + 54 \times \frac{5}{18} m s^{- 1} = + 15 m s^{- 1}

Velocity of train

B

with respect to ground

v_{BG} = - 90 km h^{- 1} = - 90 \times \frac{5}{18} m s^{- 1} = - 25 m s^{- 1}

Relative velocity of train

A

with respect to train

B

is

v_{A B} = v_{A G} + v_{GB} = v_{A G} - v_{BG} (Q v_{GB} = - v_{BG})

= + 15 m s^{- 1} - (- 25 m s^{- 1}) = 40 m s^{- 1}

Q. Two parallel rail tracks run north-south. On one track train A moves north with a speed of $54 km h^{- 1}$ and on the other track train $B$ moves south with a speed of $90 km h^{- 1}$ . The velocity of train $A$ with respect to train $B$ is

$10 m s^{- 1}$

$15 m s^{- 1}$

$25 m s^{- 1}$

$40 m s^{- 1}$

Q. Two parallel rail tracks run north-south. On one track train A moves north with a speed of 54kmh−1 and on the other track train B moves south with a speed of 90kmh−1 . The velocity of train A with respect to train B is

10ms−1

15ms−1

25ms−1

40ms−1

Q. Two parallel rail tracks run north-south. On one track train A moves north with a speed of $54 km h^{- 1}$ and on the other track train $B$ moves south with a speed of $90 km h^{- 1}$ . The velocity of train $A$ with respect to train $B$ is

$10 m s^{- 1}$

$15 m s^{- 1}$

$25 m s^{- 1}$

$40 m s^{- 1}$