When two bodies A and B are moving with velocity Av and Bv , then relative velocity of A w.r.t. B isAB A Bv v v  . Relative velocity of B w.r.t. A is  BA B A B Av v v v v     . When body C is moving withvelocity Cv on a body A, which is moving with velocity Av , then velocity of C w.r.t. ground is C Av v .Suppose two parallel rail tracks run north-south. Train A moves north with a speed of 54 kmh–1 and trainB moves south with a speed of 90 kmh–1.51. Relative velocity of ground w.r.t. B is(A) 25 ms–1 due north (B) 25 ms–1 due south(C) 40 ms–1 due north (D) 40 ms–1 due south52. A monkey is moving with a velocity 18 kmh–1 on the roof of train A against the motion of train A.The velocity of monkey as observed by a man standing on the ground is

51. The relative velocity of the ground with respect to B can be found using the formula:

Relative velocity of B w.r.t. ground = Relative velocity of B w.r.t. A + Relative velocity of A w.r.t. ground

Given that Train A moves north with a speed of 54 km/h and Train B moves south with a speed of 90 km/h, we can calculate the relative velocity of B w.r.t. ground as follows:

Relative velocity of B w.r.t. A = Bv - Av = 90 km/h - (-54 km/h) = 144 km/h

Relative velocity of A w.r.t. ground = Av = 54 km/h

Relative velocity of B w.r.t. ground = Relative velocity of B w.r.t. A + Relative velocity of A w.r.t. ground = 144 km/h + 54 km/h = 198 km/h

Converting the relative velocity from km/h to m/s:

198 km/h * (1000 m/1 km) * (1 h/3600 s) = 55 m/s

Since the relative velocity is positive, it means the ground is moving in the same direction as Train B. Therefore, the relative velocity of the ground with respect to B is 55 m/s due south.

Answer: (B) 25 m/s due south

52. The velocity of the monkey as observed by a man standing on the ground can be found using the formula:

Velocity of monkey w.r.t. ground = Velocity of monkey w.r.t. train + Velocity of train w.r.t. ground

Given that the monkey is moving with a velocity of 18 km/h on the roof of Train A, and Train A is moving north with a speed of 54 km/h, we can calculate the velocity of the monkey as observed by the man standing on the ground as follows:

Velocity of monkey w.r.t. train = 18 km/h (opposite direction to the train's motion)

Velocity of train w.r.t. ground = Av = 54 km/h

Velocity of monkey w.r.t. ground = Velocity of monkey w.r.t. train + Velocity of train w.r.t. ground = 18 km/h + 54 km/h = 72 km/h

Converting the velocity from km/h to m/s:

72 km/h * (1000 m/1 km) * (1 h/3600 s) = 20 m/s

Since the velocity is positive, it means the monkey is moving in the same direction as Train A. Therefore, the velocity of the monkey as observed by the man standing on the ground is 20 m/s.

Answer: 20 m/s