Wednesday, September 16, 2020

#213 The displacement vectors A with arrow and B

The displacement vectors A with arrow and B - Physics

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ChemistryExplain “#213 The displacement vectors A with arrow and B in Physics, Ap physics 1 practice test, Best colleges for physics, Best physics bo

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ChemistryExplain “#213 The displacement vectors A with arrow and B in Physics, Ap physics 1 practice test, Best colleges for physics, Best physics bo

The displacement vectors A with arrow and B with arrow shown in the figure below both have magnitudes of 2.22 m. The direction of vector A with arrow is 24.2°.

(a) Find A with arrow + B with arrow graphically. Find magnitude (m) and direction ° counterclockwise from the +x axis

(b) Find A with arrow − B with arrow graphically. Find magnitude (m) and direction ° counterclockwise from the +x axis

(c) Find B with arrow − A with arrow graphically. Find magnitude (m) and direction ° counterclockwise from the +x axis

(d) Find A with arrow − 2B with arrow graphically. Find magnitude (m) and direction ° counterclockwise from the +x axis

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Free Chegg Answer

Given

A = (2.22cos 24.2°î + 2.22 sin 24.2°3) m

B = (2.223) m

PART A:

C = A + B

ChemistryExplain “#213 The displacement vectors A with arrow and B in Physics, Ap physics 1 practice test, Best colleges for physics, Best physics bo

C = (2.22 cos 24.2° +2.22 sin 24.2°3) + (2.22;)

C = (2.22 cos 24.2°î + 2.22 (1 + sin 24.2°)

The magnitude of the resultant vector is

a =(2.22 cos 24.20)2 + (2.22 (1 + sin 24.2°)2) = 3.73 m

And the direction of the resultant vector is

1/2.22(1+ sin 24.2°) 0 = tan-1 2.22 cos 24.2° =5710

PART B:

C = A-3

ChemistryExplain “#213 The displacement vectors A with arrow and B in Physics, Ap physics 1 practice test, Best colleges for physics, Best physics bo

C = (2.22 cos 24.2°î +2.22 sin 24.2° 2.22

\vec C=\left (2.22\cos24.2^o\hat i+2.22\left (\sin24.2^o -1\right )\hat j \right )

The magnitude of the resultant vector is

= ((2.22 cos 24.20)2 + (2.22 (sin 24.29 – 1))?) = 2.41 m

And the direction of the resultant vector is

-1 0 = tan- 2.22 (sin 24.2° - 1) 2.22 cos 24.2° = -32.9° = (360° -32.9°) = 327.1°

Both the answers are equivalent and correct for the angle.

PART C:

\vec C=\vec B-\vec A

ChemistryExplain “#213 The displacement vectors A with arrow and B in Physics, Ap physics 1 practice test, Best colleges for physics, Best physics bo

\vec C=\left (2.22\hat j \right )-\left (2.22\cos24.2^o\hat i+2.22\sin24.2^o\hat j \right )

\vec C=\left (-2.22\cos24.2^o\hat i+2.22\left (1-\sin24.2^o \right )\hat j \right )

The magnitude of the resultant vector is

\left |\vec C \right |=\sqrt{\left (\left (-2.22\cos24.2^o \right )^2+\left (2.22\left (1-\sin24.2^o \right ) \right )^2 \right )}=2.41\ m

And the direction of the resultant vector is (it is in 2nd quadrant)

(2.22(1 - sin 24.2°) 0 = 180° + tan-1 -2.22 cos 24.20 = 180° - 32.9° = 147.1°

PART D:

\vec C=\vec A-2\vec B

ChemistryExplain “#213 The displacement vectors A with arrow and B in Physics, Ap physics 1 practice test, Best colleges for physics, Best physics bo

\vec C=\left (2.22\cos24.2^o\hat i+2.22\sin24.2^o\hat j \right )-\left (2\times 2.22\hat j \right )

\vec C=\left (2.22\cos24.2^o\hat i+2.22\left (\sin24.2^o -2\right )\hat j \right )

The magnitude of the resultant vector is

\left |\vec C \right |=\sqrt{\left (\left (2.22\cos24.2^o \right )^2+\left (2.22\left (\sin24.2^o-2 \right ) \right )^2 \right )}=4.07\ m

And the direction of the resultant vector is

\theta=\tan^{-1}\left ( \frac{2.22(\sin24.2^o-2)}{2.22\cos24.2^o} \right )=-60.2^o\equiv (360^o-60.2^o)=299.8^o

Both the answers are equivalent and correct for the angle.

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