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 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/s
What are your choices?
you have to choose true or false for each one.
To find the magnitude and x-component of V3, we can use vector addition.
V1 has a magnitude of 3.0 m/s and is directed along the +x-axis. This means its x-component is 3.0 m/s and its y-component is 0 m/s.
V2 has a magnitude of 2.0 m/s, but we don't know its direction or components yet.
To find V3, we add the x-components and the y-components of V1 and V2.
For the sum of the x-components, we have:
x-component of V3 = x-component of V1 + x-component of V2
x-component of V3 = 3.0 m/s + x-component of V2
So, the x-component of V3 can be 3.0 m/s + the x-component of V2.
For the magnitude of V3, we use the Pythagorean theorem:
magnitude of V3 = sqrt((x-component of V3)^2 + (y-component of V3)^2)
Since we know the x-component of V3, we can substitute it into the equation and simplify:
magnitude of V3 = sqrt((3.0 m/s + x-component of V2)^2 + (y-component of V3)^2)
Now, let's go through each statement and determine if it is True or False:
1. The magnitude of V3 can be -3.0 m/s:
False. The magnitude of a vector cannot be negative.
2. The x-component of V3 can be 2.0 m/s:
True. Since the x-component of V1 is 3.0 m/s and the x-component of V2 is unknown, it is possible for the x-component of V3 to be 2.0 m/s if the x-component of V2 is -1.0 m/s.
3. The magnitude of V3 can be 0.0:
False. Since V1 has a magnitude of 3.0 m/s and V2 has a magnitude of 2.0 m/s, the minimum possible magnitude for V3 is 2.0 m/s if the two vectors are in opposite directions.
4. The magnitude of V3 can be 5.0 m/s:
True. If V1 and V2 are in the same direction and their magnitudes are added, the magnitude of V3 can be 5.0 m/s (3.0 m/s + 2.0 m/s = 5.0 m/s).
5. The magnitude of V3 can be 6.0 m/s:
False. Since the magnitude of V1 is 3.0 m/s and the magnitude of V2 is 2.0 m/s, the maximum possible magnitude for V3 is 3.0 m/s + 2.0 m/s = 5.0 m/s if the two vectors are in the same direction.
6. The magnitude of V3 can be 1.0 m/s:
False. Since V1 has a magnitude of 3.0 m/s and V2 has a magnitude of 2.0 m/s, the minimum possible magnitude for V3 is 2.0 m/s if the two vectors are in opposite directions.
So, the correct statements are:
- The x-component of V3 can be 2.0 m/s.
- The magnitude of V3 can be 5.0 m/s.
On paper, draw the vector V1 (3 units to the right of origin).
From the end of vector V1, at (3,0), draw a circle of radius 2 to represent vector V2. Any point inside the circle can be the resultant of V3=V1+V2
Draw a radius, centred at the origin, of the given magnitude in each case.
If the second circle intersects or is tangential to the first, the given magnitude of V3 is possible (true). If not, it is not possible.
It is a little more work, but this will give you the insight as to how vector addition works.
The first question of magnitude -3 is a trick question, because the magnitude (length) of a vector cannot be negative.