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The velocity vector V1 has a magnitude of 4.0 m/s and is directed along the +x-axis. The velocity vector V2 has a magnitude of 3.0 m/s. The sum of the two is V3, so that V3 = V1+V2.

T/F The magnitude of V3 can be 0.0
T/F The magnitude of V3 can be 8.0 m/s
T/F The magnitude of V3 can be 7.0 m/s
T/F The magnitude of V3 can be 6.0 m/s
T/F The magnitude of V3 can be -4.0 m/s
T/F The x-component of V3 can be -1.0 m/s

User SPM
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1 Answer

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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.
User Dhruv Jagetiya
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