Final answer:
To position the 3.00 kg mass so that the center of mass is at the desired location, calculation leads to a position of approximately (-7.00 m)i + (1.33 m)j. Since this does not match any of the options given, it is necessary to recalculate or closely assess the provided options.
Step-by-step explanation:
To find where the 3.00 kg mass must be positioned so that the center of mass of the system is at (-1.00 m)i + (1.00 m)j, we can use the center of mass formula for a system of particles. This formula is Σ(mi × ri)/M, where mi is the mass of each particle, ri is the position vector of each particle, and M is the total mass of the system. We'll solve for the x and y components separately.
The x-component of the center of mass equation is (2 kg × 4.00 m + 1 kg × 1.00 m + 3 kg × x)/6 kg = -1.00 m, which simplifies to x = -7.00 m. The y-component is (2 kg × -1.00 m + 1 kg × 2.00 m + 3 kg × y)/6 kg = 1.00 m, which simplifies to y = 4.00/3 m = 1.333 m.
Therefore, to make the center of mass of the system at (-1.00 m)i + (1.00 m)j, the 3.00 kg mass must be located at (-7.00 m)i + (4.00/3 m)j or approximately (-7.00 m)i + (1.33 m)j. However, as none of the provided options exactly match this result, we need to verify our calculations or consider a possible rounding discrepancy in the answers provided