The velocity vector V1 has a magnitude of 3.0 m/s and is directed along the +x-axis. The velocity vector V2 has a magnitude of 2.0 m/s. The sum of the two is V3, so that V3 = V1+V2
true for false
The magnitude of V3 can be -3.0 m/s
The x-component of V3 can be 2.0 m/s
The magnitude of V3 can be 0.0
The magnitude of V3 can be 5.0 m/s
The magnitude of V3 can be 6.0 m/s
The magnitude of V3 can be 1.0 m
To find the sum of two vectors, V1 and V2, you can add their respective components. In this case, V1 is directed along the +x-axis, so its x-component is 3.0 m/s, and its y-component is 0 m/s. Similarly, V2 has an x-component of 2.0 m/s and a y-component of 0 m/s.
To find the x-component of V3, you add the x-components of V1 and V2: V3x = V1x + V2x = 3.0 m/s + 2.0 m/s = 5.0 m/s. Therefore, the x-component of V3 can be 5.0 m/s.
However, the magnitude of V3 can be found using the Pythagorean theorem, which states that the magnitude (or length) of a vector can be calculated by taking the square root of the sum of the squares of its components. Using this theorem, we have V3^2 = (V3x)^2 + (V3y)^2. Since V1 and V2 have no y-component, V3y = 0 m/s.
Now, we can find the magnitude of V3: V3 = sqrt((V3x)^2 + (V3y)^2) = sqrt((5.0 m/s)^2 + (0 m/s)^2) = sqrt(25.0 + 0) = sqrt(25.0) = 5.0 m/s. Therefore, the magnitude of V3 can be 5.0 m/s.
In summary, when adding vectors V1 and V2 to find V3, the x-component of V3 can be 5.0 m/s, and the magnitude of V3 can also be 5.0 m/s. Therefore, the statements "The x-component of V3 can be 2.0 m/s" and "The magnitude of V3 can be 6.0 m/s" are false.