Answer
The speed of car B just before the collision was $~~7.5~m/s$
Work Step by Step
In part (a) we found that the speed of car A when it started sliding was $~~4.6~m/s$
In part (b) we found that the speed of car B when it started sliding was $~~3.9~m/s$
We can use conservation of momentum to find the speed of car B just before the collision:
$p_i = p_f$
$(1400~kg)~v_i = (1100~kg)(4.6~m/s)+(1400~kg)(3.9~m/s)$
$v_i = \frac{(1100~kg)(4.6~m/s)+(1400~kg)(3.9~m/s)}{1400~kg}$
$v_i = 7.5~m/s$
The speed of car B just before the collision was $~~7.5~m/s$
