A position vector r vector has the following x and y components: r_x = 13.4 m r_

Question

A position vector r vector has the following x and y components: r_x = 13.4 m r_y = 8.2 m. (a) What is the direction of this vector? Give your answer as an angle measured counterclockwise from the +x direction. Degree (b) What is the magnitude of this vector? m (c) If you doubled both the x and y components of this vector, how would the answers to parts (a) and (b) change? The angle counterclockwise from +x would increase by a factor of 2, but the magnitude would remain the same. The direction would remain the same, but the magnitude would increase by a factor of 2. The direction would remain the same, but the magnitude would increase by a factor of 4. The direction of the vector would rotate clockwise by an angle equal to twice the angle measured counterclockwise from +x, but the magnitude would remain the same. Determine the magnitude and direction of the vector A vector = (-27.5)i^+ (44.2)j^. |A vector| = alpha = degree counterclockwise from the +x axis

Explanation / Answer

1

(a) direction=tan^(-1)(ry/rx)=31.5 degrees

(b)magnitude=sqrt(rx^2+ry^2)=15.7 m

(c)if it is doubled

direction will be same as ry/rx will be same

magnitude will be doubled as both rx and ry are doubled

option (b) is correct

2

|A|=52.05

angle=121.89 degrees

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