Treatment Systems: Radon Tipsheet #6 Reduce Air Radon Levels in
Vectors Tipsheet 2020 · = population standard deviation Median - The middle value. This is...
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Vectors STEP 1: DECOMPOSE THE VECTORS A vector is a quantity that has both magnitude and direction. For example, displacement, velocity, acceleration, and force are all vectors, as each of these quantities have a magnitude and direction associated with them. To add vectors, they must first be decomposed into their x- and y- components. Like components are then added together. The resultant vector is then recomposed to determine its magnitude and direction. Example: Two vectors, A and B, are shown in the figure below. Find the resultant vector, R = A + B , and include its direction as an angle from the positive x-axis. SOH CAH TOA can now be used to determine B x and B y. Since B x is pointing left and B y is pointing upward, the x-component is negative and the y-component is positive. 30° 386 N 523 N B A 45° 30° 386 N A y A A x B x B y B A x A x = 386 cos(30°) A x = 334 N = 370 N B x = 523 cos(45°) = 370 N B y = 523 sin(45°) A y = 386 sin(30°) A y = 193 N adj hyp 386 A y opp hyp 386 523 N 45° SOH CAH TOA can be used to determine A x and A y. Since A x is pointing right and A y is pointing upward, both the x- and y-components are positive. cos(30°) sin(30°) sin(30°) cos(30°)
Transcript of Vectors Tipsheet 2020 · = population standard deviation Median - The middle value. This is...
Vectors
STEP 1: DECOMPOSE THE VECTORS
µ = population means2 = variance of sample
= population standard deviation
Median - The middle value. This is calculated by �nding the position of the median and then locating that position on your data set.
Formula for position of median: (n + 1) / 2
A vector is a quantity that has both magnitude and direction. For example, displacement, velocity, acceleration, and force are all vectors, as each of these quantities have a magnitude and direction associated with them.
To add vectors, they must �rst be decomposed into their x- and y- components. Like components are then added together. The resultant vector is then recomposed to determine its magnitude and direction.
Example: Two vectors, A and B, are shown in the �gure below. Find the resultant vector, R = A + B , and include its direction as an angle from the positive x-axis.
SOH CAH TOA can now be used to determine Bx and By. Since Bx is pointing left and By is pointing upward, the x-component is negative and the y-component is positive.
30°
386 N
523 NB
A
45°
30°
386 N
Ay
A
Ax
Bx
By
B
Ax
Ax = 386 cos(30°)
Ax = 334 N
= 370 NBx = 523 cos(45°)
= 370 NBy = 523 sin(45°)
Ay = 386 sin(30°)
Ay = 193 N
adjhyp
386Ay
opphyp
386
523 N
45°
SOH CAH TOA can be used to determine Ax and Ay. Since Ax ispointing right and Ay is pointing upward, both the x- and y-componentsare positive.
cos(30°) sin(30°)
sin(30°)cos(30°)
To determine the resultant vector, R, use vector addition to �nd Rx + Ry. Since these vectors are perpendicular, Pythagorean Theorem may be used to calculate the magnitude of R. SOH CAH TOA can then be used to determine the direction of R.
Rx Ry
( 36) (563)
STEP 2: ADD LIKE COMPONENTS
STEP 3: RECOMPOSE THE VECTOR
θΦ
tan =564 N
36 N
563 N
Rx = Ax + Bx
= 334 + ( 370) = 36 N
Ry = Ay + By
= 193 + 370 = 563 N
Magnitude of R:
Direction of R:
Rx
Ry
R +
+= 564 N
=
= 2 2
2 2
R θ
tan =θ
= tan-1
= tan-1
= 86.3°
To determine the angle from the positive x-axis, , subtract from 180°.
Therefore the resultant vector is:
θ
= 180° 86.3°
= 93.7°
R = 564 N [93.7° CCW from the positive x-axis]
oppadj
RyRx
RyRx
56336
Φ
ΦΦ
θ
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