Explore In each case below, calculate the indicated quantities using thefollowin

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In each case below, calculate the indicated quantities using thefollowing vectors.

vector

x-component

y-component

A

1.38 m

-2.55 m

B

-3.37 m

-4.02 m

C

2.72 m

8.53 m

Use the animation at right to represent each calculationgraphically. Indicate all direction angles measuredcounter-clockwise from the positive x-axis.

(a) What is A + B?

Magnitude: 1 m
Direction: 2°

(b) What is A - B?

Magnitude: 3 m
Direction: 4°

(c) What is A + B +C?

vector

x-component

y-component

A

1.38 m

-2.55 m

B

-3.37 m

-4.02 m

C

2.72 m

8.53 m

Explanation / Answer

vector

x-component

y-component

A

1.38 m

-2.55 m

B

-3.37 m

-4.02 m

C

2.72 m

8.53 m

(a) What is A + B?

Magnitude: 1 m
Direction: 2°

A+B=(1.38-3.37)2+(-2.55-4.02)2=3.9601+43.1649=6.8647m

direction==73.14degree.

(b) What is A - B?

Magnitude: 3 m=(1.38+3.37)2+(-2.55+4.02)2=4.752+1.472=4.97201m
Direction: 4°=17.19degree.

(c) What is A + B +C?

vector

x-component

y-component

A

1.38 m

-2.55 m

B

-3.37 m

-4.02 m

C

2.72 m

8.53 m

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