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
A. The x-component of V3 can be 3.0 m/s
B. The magnitude of V3 can be 8.0 m/s
C. The magnitude of V3 can be 4.0 m/s
D. The magnitude of V3 can be -6.0 m/s
E The magnitude of V3 can be 0.0
F The magnitude of V3 can be 7.0 m/s
Its asking which if A-F are true or false.
F. V3 = 4 + 3 = 7.
To add them directly, both must be on the X-axis.
To determine which statements are true or false, let's analyze the given information:
1. Velocity vector V1 has a magnitude of 4.0 m/s and is directed along the +x-axis.
2. Velocity vector V2 has a magnitude of 3.0 m/s.
Now let's calculate the sum of the two velocity vectors:
V3 = V1 + V2
Since V1 is directed along the +x-axis, its y-component is zero, and its x-component is 4.0 m/s.
Since V2's direction is not specified, let's assume it is in any direction except along the -x-axis, as that would make the sum V3 zero.
Let's break down V2 into its x-component (V2x) and y-component (V2y) using the given magnitude of 3.0 m/s:
V2x = V2 * cos(theta)
V2y = V2 * sin(theta)
where theta is the angle between V2 and the +x-axis.
Since the direction of V2 is not specified, we will ignore its y-component for now.
Now we can add the x-components of V1 and V2:
V3x = V1x + V2x = 4.0 m/s + V2x
Based on this analysis, we can conclude:
A. The x-component of V3 can be 3.0 m/s: False, as the x-component of V3 includes the unknown x-component of V2 (V2x).
B. The magnitude of V3 can be 8.0 m/s: False, as the magnitude of V3 depends on both its x and y-components.
C. The magnitude of V3 can be 4.0 m/s: False, as the magnitude of V3 is not limited to the magnitude of V1.
D. The magnitude of V3 can be -6.0 m/s: False, as the magnitude is always a positive value.
E. The magnitude of V3 can be 0.0: False, as the magnitude of V3 is dependent on the magnitudes of V1 and V2.
F. The magnitude of V3 can be 7.0 m/s: True, as the magnitude of V3 can be calculated once we know the x and y-components.
Therefore, the only statement that is true is F. The magnitude of V3 can be 7.0 m/s.