Answer
At $t = 2.80~s$, the velocity of block C is $~~-0.15~m/s$
Work Step by Step
Note that the initial momentum of the system is 0 because $v_i = 0$
We can use conservation of momentum to find the velocity $v_1$ of block C after block L is shot to the left:
$p_f = p_i$
$(2.00)(v_1-3.00)+(8.00)(v_1) = 0$
$10.00~v_1-6.00 = 0$
$v_1 = 0.60~m/s$
We can use conservation of momentum to find the velocity $v_2$ of block C after block R is shot to the right:
$(2.00)(v_2+3.00)+(6.00)(v_2) = 8.00~v_1$
$8.00~v_2+6.00 = 4.80$
$8.00~v_2 = -1.20$
$v_2 = -\frac{1.20}{8.00}$
$v_2 = -0.15~m/s$
At $t = 2.80~s$, the velocity of block C is $~~-0.15~m/s$
