Answer
The speed of the two-cart center of mass is $~~0.93~m/s$
Work Step by Step
In part (a), we found that the mass of the second cart is $98.7~g$
In part (b), we found that the speed of the second cart after impact is $~~1.86~m/s$
We can find the speed of the two-cart center of mass:
$v_{com} = \frac{(340~g)(0.66~m/s)+(98.7~g)(1.86~m/s)}{340~g+98.7~g}$
$v_{com} = 0.93~m/s$
The speed of the two-cart center of mass is $~~0.93~m/s$
