Directions are measured counter-clockwise from the positive x axis. Vector A has

Question

Directions are measured counter-clockwise from the positive x axis. Vector A has an x-component 15, and a y-component 8. Vector B is in the direction 153.4°, and has an x-component 4. Vector has a magnitude 20, and its direction is 203.6°. Vector D has a magnitude of 17, and its x and y components are equal in magnitude. The y component of D is negative, and its x component is positive. What is the magnitude of vector A? O 23 17 O none of the given answers Question2 10 pts What is the magnitude of vector B? O cannot be determined from the information given O 12 O the square root of 20

Explanation / Answer

Question -1

Vector A = 15i + 8j

=> |A| = sqrt[15^2 + 8^2] = 17

Hence third option '17' is the correct answer.

Question -2:

|B|*cos153.4 = -4

=> |B| = -4 / cos153.4 = 4.47 = sqrt[20]

|B|sin153.4 = 4.47*sin153.4 = 2.0

Vector B = -4i + 2j

hence option third 'square root of 20' is the correct answer.

Question -3:

Vector C = 20*cos203.6i + 20*sin203.6j = -18.33i - 8.0j

so y-component = -8

so, second option '-8' is the correct answer.

Question - 4:

x-component of vector C = -18.3

hence third option '-18.3' is the correct answer.

Question -5 -

Vector D = 17*cos315i + 17*sin315j = 12.02i - 12.02j

so fourth option '315 deg' is the correct answer.

Question -6 -

Direction of vector A = tan^-1(8/15) = 28.07 deg

so, first option '28 deg' is the correct answer.

Question -7 -

Y- component of vector D = -12.02

So, last option, '-12' is the correct answer.

Question -8 -

A + B + C + D = 15i + 8j -4i + 2j -18.33i - 8.0j +12.02i - 12.02j =  4.69i - 10.02j

X - component = 4.69 = 4.7

hence second option '4.7' is the correct answer.

Question -9 -

Y - component = -10.02

hence fourth option '-10' is the correct answer.

Question -10 -

theta = tan^-1(-10.02 / 4.69) = -65 deg = 360-65 = 295 deg.

Fourth option '295 deg' is the correct answer.

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