The vector position of a 3.80 g particle moving in the xy plane varies in time according to the following equation.

Question

r1=(3i+3j)t+2jt^2

At the same time, the vector position of a 5.35 g particle varies according to the following equation.

r2=3i-2it^2-6jt

For each equation, t is in s and r is in cm. Solve the following when t = 2.60
(a) Find the vector position of the center of mass.(i+j)

Answer 1

Use your equations to get the vector locations of each particle at t = 2.60.
Call then (X1,Y1) and (X2,Y2) (or X1i + XY1j and X2i + Y2j))

The X and Y coordinates of the CM will be the mass-weighted mean location:

Xcm = (M1 X1 + M2 X2)/(M1 + M2)
etc.