(a) Using conservation of momentum for the collision between P and Q:

The initial momentum is given by:

\(0.3 \times 4 + 0 = 1.2 \text{ kg m s}^{-1}\)

The final momentum is:

\(0.3v + 0.2 \times 3\)

Equating initial and final momentum:

\(1.2 = 0.3v + 0.6\)

Solving for \(v\):

\(0.3v = 0.6\)

\(v = 2 \text{ m s}^{-1}\)

(b) Using conservation of momentum for the collision between Q and R:

The initial momentum is given by:

\(0.2 \times 3 + 0 = 0.6 \text{ kg m s}^{-1}\)

The final momentum is:

\((0.2 + m) \times 2\)

Equating initial and final momentum:

\(0.6 = (0.2 + m) \times 2\)

Solving for \(m\):

\(0.6 = 0.4 + 2m\)

\(0.2 = 2m\)

\(m = 0.1 \text{ kg}\)