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Anuta_ua [19.1K]
2 years ago
13

Find out the x-component and y-component of the following vectors:

Physics
2 answers:
Nina [5.8K]2 years ago
8 0
<h2>Answer:</h2><h2></h2>

The x- and y- components of vector A are -12.99cm and 7.5cm respectively.

The x- and y- components of vector B are 7.71m and 9.20m respectively.

The x- and y- components of vector C are -21.45m/s and -18.00m/s respectively.

The x- and y- components of vector D are 22.94m/s² and -16.06m/s² respectively.

<h2>Explanation:</h2><h2></h2>

Given an arbitrary vector M (written in bold face), of magnitude M (not written in bold face), which makes an angle θ to the positive x axis, the x-component of M (written as M_{X}) is given by;

M_{X} = M cos θ

And its y-component (written as M_{Y}) is given by;

M_{Y} = M sin θ

Therefore, taking due east as positive x axis, for the vector:

<em>(i) A = 15.0 cm; the vector is 30.00 north of west; </em>

the x-component of A (written as A_{X}) is given by;

A_{X} = A cos θ            --------------------(i)

And its y-component (written as A_{Y}) is given by;

A_{Y} = A sin θ              --------------------(ii)

<em>Where;</em>

A = 15.0cm

θ = 30.00 north of west =  180° - 30.00° [measured due east] = 150°

<em>Substitute these values into equations (i) and (ii) as follows;</em>

A_{X} = 15.0 cos 150° =  15.0 x -0.8660 = -12.99cm      

A_{Y} = 15.0 sin 150° = 15.0 x 0.5 = 7.5cm

Therefore, the x- and y- components of vector A are -12.99cm and 7.5cm respectively.

<em>(ii) B = 12.0 m; the vector is 55.00 north of east; </em>

the x-component of B (written as B_{X}) is given by;

B_{X} = B cos θ            --------------------(iii)

And its y-component (written as B_{Y}) is given by;

B_{Y} = B sin θ              --------------------(iv)

<em>Where;</em>

B = 12.0m

θ = 55.0 north of east =  50° [measured due east]

<em>Substitute these values into equations (iii) and (iv) as follows;</em>

B_{X} = 12.0 cos 50° =  12.0 x 0.6428 = 7.71m      

B_{Y} = 12.0 sin 50° = 12.0 x 0.7660 = 9.20m

Therefore, the x- and y- components of vector B are 7.71m and 9.20m respectively.

<em>(iii) C = 28.0 m/s; the vector is 40.00 south of west; </em>

the x-component of C (written as C_{X}) is given by;

C_{X} = B cos θ            --------------------(v)

And its y-component (written as C_{Y}) is given by;

C_{Y} = B sin θ              --------------------(vi)

<em>Where;</em>

C = 28.0m/s

θ = 40.00 south of west =  180° + 40.00° [measured due east] = 220°

<em>Substitute these values into equations (v) and (vi) as follows;</em>

C_{X} = 28.0 cos 220° =  28.0 x -0.7660 = -21.45m/s

C_{Y} = 28.0 sin 220° = 28.0 x -0.6428 = -18.00m/s

Therefore, the x- and y- components of vector C are -21.45m/s and -18.00m/s respectively.

<em>(iv) D = 55.5 m/s²; the vector is 35.00 south of east; </em>

the x-component of D (written as D_{X}) is given by;

D_{X} = D cos θ            --------------------(vii)

And its y-component (written as D_{Y}) is given by;

D_{Y} = D sin θ              --------------------(viii)

<em>Where;</em>

D = 55.5m/s²

θ = 35.00 south of east =  360° - 35.00° [measured due east] = 325°

<em>Substitute these values into equations (vii) and (viii) as follows;</em>

D_{X} = 55.5 cos 325° =  28.0 x 0.8192 = 22.94m/s²

D_{Y} = 55.5 sin 325° = 28.0 x -0.5736= -16.06m/s²

Therefore, the x- and y- components of vector D are 22.94m/s² and -16.06m/s² respectively.

Leno4ka [110]2 years ago
6 0

Answer:

A = 15.0 cm; the vector is 30.00 north of west; = 15 cm N30W

Y - component = 7.5cm and X - component = -12.99 cm

B = 12.0 m; the vector is 55.00 north of east; = 12.0 m N55E

Y - component = 9.83 m and X - component = 6.88 m

C = 28.0 m/s; the vector is 40.00 south of west; = 28.0 m/s S40W

Y - component =  - 17.998 m/s and X - component = - 21.448 m/s

D = 55.5 m/s2; the vector is 35.00 south of east; = 55.5 m/s² S35E

Y - component = - 31.835 m/s² and X - component  = 45.466 m/s²

Explanation:

1. A = 15.0 cm; the vector is 30.00 north of west; = 15 cm N30W

Y - component = 15cm × sin30 = 7.5cm

X - component = -15cm × cos30 = -12.99 cm

2. B = 12.0 m; the vector is 55.00 north of east; = 12.0 m N55E

Y - component = 12.0 m × sin55 = 9.83 m

X - component =12.0 m × cos55 = 6.88 m

3. C = 28.0 m/s; the vector is 40.00 south of west; = 28.0 m/s S40W

Y - component = - 28.0 m/s × sin40 = - 17.998 m/s

X - component =  - 28.0 m/s × cos40 = - 21.448 m/s

4. D = 55.5 m/s2; the vector is 35.00 south of east; = 55.5 m/s² S35E

Y - component = - 55.5 m/s² × sin35 = - 31.835 m/s²

X - component = 55.5 m/s² × cos35 = 45.466 m/s²

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Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

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P(5.675

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P(5.675

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P(-1.83

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