partscoretotalsubmissions1--10/12--10/13--10/14--10/1----4--The tail of a vector is fixed to the origin of an x, y axis system. Originally the vector points along the +x axis. As time passes, the vector rotates counterclockwise. Describe how the sizes of the x and y components of the vector compare to the size of the original vector for the following rotational angles. (Select all that apply.)
(a) 90°
x has zero magnitude
y has zero magnitude
magnitude of x components is equal to magnitude of the original vector
magnitude of y components is equal to magnitude of the original vector
(b) 180°
x has zero magnitude
y has zero magnitude
magnitude of x components is equal to magnitude of the original vector
magnitude of y components is equal to magnitude of the original vector
(c) 270°
x has zero magnitude
y has zero magnitude
magnitude of x components is equal to magnitude of the original vector
magnitude of y components is equal to magnitude of the original vector
(d) 360°
x has zero magnitude
y has zero magnitude
magnitude of x components is equal to magnitude of the original vector
magnitude
I believe it is as follows:
a) x=0
b) y=0
the mag of x would be equal, but in the neg directioin
c)x=0
and the mag of x is = to the origional
d) all apply except mag of x does not equal 0
as a disclaimer i did not do the math to solve this, but you could use trig to check these answers
Baba ji ka thullu
The sizes of the x and y components of the vector can be described as follows for the given rotational angles:
(a) 90°:
- x has zero magnitude
- y has a magnitude equal to the magnitude of the original vector
(b) 180°:
- x has zero magnitude
- y also has zero magnitude
(c) 270°:
- x has zero magnitude
- y has a magnitude equal to the magnitude of the original vector
(d) 360°:
- x has zero magnitude
- y also has zero magnitude
So, the correct descriptions for the sizes of the x and y components are:
(a) y has zero magnitude; magnitude of x components is equal to magnitude of the original vector
(b) x has zero magnitude; y has zero magnitude
(c) y has zero magnitude; magnitude of x components is equal to magnitude of the original vector
(d) x has zero magnitude; y has zero magnitude
To determine how the sizes of the x and y components of the vector compare to the size of the original vector for different rotational angles, we can use some basic trigonometry.
When a vector points along the +x axis, its x component is equal to the magnitude of the vector, and its y component is zero.
As the vector rotates counterclockwise, its x and y components change. To find the x and y components of the vector after rotation, we can use the trigonometric functions sine and cosine.
Let's analyze each rotational angle:
(a) 90° rotation:
At this angle, the vector would be pointing along the +y axis. This means that the x component would have zero magnitude, while the y component would have the same magnitude as the original vector. Therefore, the correct choices are:
- x has zero magnitude
- y components is equal to magnitude of the original vector
(b) 180° rotation:
At this angle, the vector would be pointing in the opposite direction of the +x axis. Both the x and y components would have zero magnitude. Therefore, the correct choices are:
- x has zero magnitude
- y has zero magnitude
(c) 270° rotation:
At this angle, the vector would be pointing along the -y axis. This means that the x component would have zero magnitude, while the y component would have the same magnitude as the original vector. Therefore, the correct choices are:
- x has zero magnitude
- y components is equal to magnitude of the original vector
(d) 360° rotation:
At this angle, the vector would have completed one full rotation and would be pointing along the +x axis again, just like the original vector. Therefore, both the x and y components would have the same magnitude as the original vector. Therefore, the correct choices are:
- magnitude of x components is equal to magnitude of the original vector
- magnitude of y components is equal to magnitude of the original vector
In summary:
(a) 90°: x has zero magnitude, y components is equal to magnitude of the original vector
(b) 180°: x has zero magnitude, y has zero magnitude
(c) 270°: x has zero magnitude, y components is equal to magnitude of the original vector
(d) 360°: magnitude of x components is equal to magnitude of the original vector, magnitude of y components is equal to magnitude of the original vector