Question

An elevator moving down passes its neighbor, an elevator moving up. Their speed relative to one another is 8 m/s. What is the velocity of each elevator relative to someone standing on the first floor? Assume that the elevators are traveling at the same speed, and that the upward direction is positive.

Answer 1

LiftA= u m/s ( upwards)
LiftB= -u m/s(downward)

Velocity A relative to B= V lift A- V lift B=8m/s
u-(-u)=8
u=4m/s
Lift A= 4 m/sec
Lift B= -4m/sec
For someone standing on first floor will be stationary W.r.t to the lift.
V lift A relative to Man= V liftA - V man= 4m/s

V lift B relative to Man= V lift B- V Man= -4 m/s

Answer 2

If they appear to be travelling at 8 m/s as viewed by one of them, then someone on ground floor sees what is actually happening. One is going up at 4 m/s and the other is going down at 4 m/s.

The direction matters. The answer is C.