Vector À, vector B, and vector are drawn to scale in the figure below. The vecto
ID: 1573955 • Letter: V
Question
Vector À, vector B, and vector are drawn to scale in the figure below. The vector A is 5.3 meters long and points 56 counterclockwise from the positive axis. The vector B is 4.0 meters long and points along the negative r-axis. The vector C is 2.8 meters long and points 53° clockwise from the negative z-axis. What are Rand R the magnitude and direction angle for the resultant vector R-A+B+ Constants Click Play to watch the video below. Answer the ungraded questions in the video and the graded follow-up questions at right. Comçonent Method Express your answer numerically in metersand degrees respectively as the ordered pair R, using three significant figures. Measure the angle counterclockwise from the positive z-axis. igure R, BR 1 of 1 Submit X Incorrect; Try Again; 4 attempts remaining The submitted answer reports the magnitude of R as being less than the magnitude of the component vector Ry. The hypotenuse of a right triangle must be longer than either of the other two sides. When applying the Pythagorean theorem, recall that the square of a negative number is positive. Next >Explanation / Answer
Rx = A*cos(56) - B - C*cos(53)
= 5.3*cos(56) - 4 - 2.8*cos(53)
= -2.72 m
Ry = A*sin(56) - 0 + C*sin(53)
= 5.3*sin(56) - 0 + 2.8*sin(53)
= 6.63 m
R = sqrt(Rx^2 + Ry^2)
= sqrt(2.72^2 + 6.63^2)
= 7.17 m <<<<<<<<----------------Answer
theta_R = tan^-1(Ry/Rx)
= tan^-1(6.63/(-2.72))
= 68.0 degrees with -x axis in clockwise direction.
= 180 - 68.0
= 112 degrees with +x axis in counter clockwise direction <<<<<<<<----------------Answer
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