Question

The x & y components of a vector r are rx= 16m and ry=-8.5m. A. Find the direction of the Vector, r. B. Find the magnitude of the Vector, r. C. Suppose that rx and ry are doubled, find the direction and magnitude of the new Vector, r. D. Find r' using the answer from Part B and express your answer in two significant figures.

Answer 1

A)Direction is $tan^{-1}\frac{r_y}{r_x}=tan^{-1}\frac{-8.5}{16}=332.02\degree$ ccw of +x axis

B)Magnitude is $\sqrt{16^2+(-8.5)^2}=18.12m$

C)f magnitude is doubled direction remains the same as the ratio of y to x component remains the same.

D)Magnitude is $2\times18.12m=36m$ correct to 2 significant figures