So I wrote down my answer, but I am not sure if I did the significant figures ri

Question

So I wrote down my answer, but I am not sure if I did the significant figures right. Can you confirm?

For example, to find the magnitude of the vector ( square root of (41.3)^2 + (39)^2), or to find the angle, (arctan (39/41.3)), how do I go about significant figures there?

QUESTION 7 Two force vectors lie in a plane described by x-y coordinates. Force A is 22.4 N at 33.0° with respect to (w.r.t.) the x-axis [angles measured in the usual counter-clockwise direction], and force B is 35.0 N at 50.0° w.r.t. the x-axis. (Use proper number of significant figures). The y-component of A (Ay) is N. 12.2 QUESTION8 Two force vectors lie in a plane described by x-y coordinates. Force A is 22.4 N at 33.0° with respect to (w.r.t.) the x-axis [angles measured in the usual counter-clockwise direction], and force B is 35.0 N at 50.0° w.r.t. the x-axis. (Use proper number of significant figures). The magnitude of the vector sum of these vectors (R A+B; the magnitude is labeled R) i:s N. 56.8 QUESTION 9 Two force vectors lie in a plane described by x-y coordinates. Force A is 22.4 N at 33.0° with respect to (w.r.t.) the x-axis [angles measured in the usual counter-clockwise direction], and force B is 35.0 N at 50.0° w.r.t. the x-axis. (Use proper number of significant figures). The direction of R, specified as an angle w.rt, the x-axis, is degrees. 43.4

Explanation / Answer

Ax = 22.4*cos 33 deg = 18.786 = 18.8

Ay = 22.4*sin 33 deg = 12.1999 = 12.2 (Q7)

Bx = 35*cos 50 deg = 22.497 = 22.5

By = 35*sin 50 deg = 26.811 = 26.8

A + B = Ax + Ay + Bx + By

A + B = (Ax + Bx)i + (Ay + By)j

A + B = (18.8 + 22.5) + (12.2 + 26.8)

A + B = 41.3 i + 39.0 j

|A + B| = sqrt (41.3^2 + 39.0^2) = 56.803 = 56.8

Now

Angle = arctan (39.0/41.3) = 43.359 = 43.4 deg

About significant figures

If we add or divide two numbers then in the final Answer significant number will be same as minimum significant in the given numbers.

E.g. 23.3 + 27.78 = 51.08 = 51.1

in your answer we will use 39.0 and not 39, since in 22.4 and 35.0 significant numbers are 3, So in final answer significant number should be 3

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