Two parallel rail tracks run north-south. Train A moves north . . .

Question : Two parallel rail tracks run north-south. Train A moves north with a speed of 54 km/h, and train B moves south with a speed of 90 km/h. What is the 

a) velocity of B with respect to A?
b) velocity of ground with respect to B?, and 
c) velocity of monkey running on the roof of the train A against its motion (with a velocity of 18 km/h with respect to the train A) as observed by a man standing on the ground?

Doubt by Faisal

Solution : 
VA= 54 km/h (North)
VA = +54×(5/18) m/s
VA = +15 m/s
[Positive sign is used to denote the North direction]

VB = 90 km/s (South)
VB = -90×(5/18)
VB = -25 m/s
[Negative sign is used to denote the North direction]

a) Velocity of B w.r.t. A 
=VBA
=VB-VA
= -25-(15)
= -25-15
= -40 m/s
The -ve sign shows that the train B appears to move towards the south direction for an observer in train A.

b) Velocity of ground (VG) = 0 m/s
[Ground is stationary this is why it's velocity is taken as zero]

Velocity of ground with respect to B
= VGB
= VG-VB
= 0-(-25)
= 0+25
= 25 m/s

The positive value shows that for an observer in train B the ground is appear to move towards the north direction. 

c)  velocity of monkey running on the roof of the train A against its motion (with a velocity of 18 km/h with respect to the train A) as observed by a man standing on the ground?

Train A is going towards North and the monkey is moving against it motion i.e. the monkey is moving towards south.

VMA =  18 km/h (South)
VMA = -18×(5/18) m/s
VMA = - 5 m/s
The -ve shows that monkey is moving in the opposite direction of observer in train A.

VA = +15 m/s
VMA = - 5 m/s
VM-VA=-5
VM-15=-5
VM=-5+15
VM=+10 m/s

Velocity of man standing on the ground will be zero. 
VMan = 0 m/s

So 
VMMan = VM-VMan
VMMan = 10-0
= +10 m/s

Positive sign shows that the for a stationary man standing on the ground the monkey is going towards the north direction.