Given the following vectors, find the x and y components
a.
Ᾱ = 37 m with an angle of 25°
b.
? = 16m with an angle of 90°
c.
? = 25m with an angle of 0°
d.
? = 30m with an angle of 180°
ADD AND SUBTRACT THE FOLLOWIN VECTORS PAIRS
HINT: You have already solved the x and y components in section I.
a.
Add: = 37m at 25°&= 16m at 90°
b.
Add: = 25 m at 0°&= 30m at 180°
c.
Add: = 37m at 25°&= 30m at 180°
d.
Add: = 16m at 90°&=25m at 0°
e.
Subtract: = 37m at 25°&= 16m at 90°
f.
Subtract: = 25 m at 0°&= 30m at 180°
g.
Subtract: = 37m at 25°&= 30m at 180°
h.
Subtract: = 16m at 90°&=25m at 0°
i.
Add: (1,2,3) + (-4,5,-6)
j.
Subtract: (1,2,3) – (-4,5,-6)
a.
Vx = 37 cos 25
Vy = 37 sin 25
b.
Vx = 16 cos 90
Vy = 16 sin 90
etc
To find the x and y components of a vector, you can use trigonometry. The x component can be found by multiplying the magnitude of the vector by the cosine of the angle, and the y component can be found by multiplying the magnitude by the sine of the angle.
a. Given the vector Ᾱ = 37 m with an angle of 25°:
x component = 37 m * cos(25°)
y component = 37 m * sin(25°)
b. Given the vector ? = 16 m with an angle of 90°:
x component = 16 m * cos(90°)
y component = 16 m * sin(90°)
c. Given the vector ? = 25 m with an angle of 0°:
x component = 25 m * cos(0°)
y component = 25 m * sin(0°)
d. Given the vector ? = 30 m with an angle of 180°:
x component = 30 m * cos(180°)
y component = 30 m * sin(180°)
To add vectors, you can simply add their x components together and their y components together:
a. Add: Ᾱ + ? = (x component of Ᾱ + x component of ?) + (y component of Ᾱ + y component of ?)
b. Add: ? + ? = (x component of ? + x component of ?) + (y component of ? + y component of ?)
c. Add: Ᾱ + ? = (x component of Ᾱ + x component of ?) + (y component of Ᾱ + y component of ?)
d. Add: ? + ? = (x component of ? + x component of ?) + (y component of ? + y component of ?)
To subtract vectors, you can simply subtract their x components and their y components:
e. Subtract: Ᾱ - ? = (x component of Ᾱ - x component of ?) - (y component of Ᾱ - y component of ?)
f. Subtract: ? - ? = (x component of ? - x component of ?) - (y component of ? - y component of ?)
g. Subtract: Ᾱ - ? = (x component of Ᾱ - x component of ?) - (y component of Ᾱ - y component of ?)
h. Subtract: ? - ? = (x component of ? - x component of ?) - (y component of ? - y component of ?)
i. To add the vectors (1,2,3) and (-4,5,-6), simply add the corresponding components together:
(1,2,3) + (-4,5,-6) = (1 + (-4), 2 + 5, 3 + (-6))
j. To subtract the vectors (1,2,3) and (-4,5,-6), simply subtract the corresponding components:
(1,2,3) - (-4,5,-6) = (1 - (-4), 2 - 5, 3 - (-6))