Answer
The speed of the other block is $~~0.57~m/s$
Work Step by Step
It is given in the question that the velocity of the center of mass is $v_{com} = 0$
We can find the initial velocity $v_i$ of the other block:
$v_{com} = \frac{(1.0~kg)(1.7~m/s)+(3.0~kg)(v_i)}{1.0~kg+3.0~kg}$
$0 = \frac{(1.0~kg)(1.7~m/s)+(3.0~kg)(v_i)}{1.0~kg+3.0~kg}$
$0 = (1.0~kg)(1.7~m/s)+(3.0~kg)(v_i)$
$-(3.0~kg)(v_i) = (1.0~kg)(1.7~m/s)$
$v_i = -\frac{(1.0~kg)(1.7~m/s)}{3.0~kg}$
$v_i = -0.57~m/s$
The speed of the other block is $~~0.57~m/s$
