There is a pulley system as shown in the figure. It is used in a game of tug-of-war. The team A pulls the rope so that the rope at their end is pulled at 3m/s. What is the velocity at which the team B will be pulled.

1) 0.2 m/s.
2) 5 m/s.

3) 0.5 m/s.
4) 2 m/s.

Position Coordinate equation-
The positions of team A and team B are defined using coordinates SA and SB.A third coordinate Sc is used to relate the two coordinates SA and SB.

The equations for the cord lengths are given by
SA + 2SC = l1.
2SB + (SB-SC) = l2.
Eliminating Sc and combining the two equations,
SA + 6SB = l1 + l2.

Time Derivative-
The time derivative gives,
VA + 6VB = 0,

When VA = 3 m/s,(towards left)
VB = 0.5 m/s.
(towards right)
This is the velocity at which team B will be pulled toward right.