Final answer:
The magnitude of V3 cannot be 0.0 or 8.0 m/s due to the given magnitudes of V1 and V2. The magnitude of V3 could potentially be 7.0 m/s, and the maximum value must be less than 7.0 m/s given their directions are not specified. The x-component of V3 could be -1.0 m/s if V2 is directed oppositely to V1.
Step-by-step explanation:
When dealing with vector addition, the magnitude of the resultant vector depends on both the magnitudes and directions of the original vectors. The velocity vector V1 has a magnitude of 4.0 m/s along the +x-axis and velocity vector V2 has a magnitude of 3.0 m/s, which could have any direction. To find the resultant vector V3, the direction of V2 relative to V1 is crucial.
- The magnitude of V3 can be 0.0 m/s if V2 is equal in magnitude but opposite in direction to V1 along the x-axis.
- The magnitude of V3 could be as large as 7.0 m/s if V2 is directed at an angle to V1 or as small as greater than 1.0 m/s if it is directed completely opposite to V1.
- The magnitude of V3 cannot be 8.0 m/s because this would require that V2 also act entirely along the x-axis in the same direction as V1, but V2's magnitude (3.0 m/s) is insufficient to reach a total of 8.0 m/s with V1's 4.0 m/s.
- The magnitude of V3 cannot be -4.0 m/s because magnitudes of vectors are always non-negative.
- The x-component of V3 could be -1.0 m/s if V2 is 3.0 m/s in the negative x-direction.