Physics Vectors Help!!! Am I supposed to somehow use the Pythagorean theorem to answer this? I've tried multiple times to answer, but what is the best way to solve this sort of problem???

Question

1441 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-18T18:36:21

Consider that,

$- \to M$ $vec M$ is the sum of $\to P$ $vec P$ and $\to Q$ $vec Q$ . Moreover, consider that,

$\to P$ $vec P$ and $\to Q$ $vec Q$ have been resolved into their components in the question. With this data, we may find the magnitude via,

$V = \sqrt{V_{x}^{2} + V_{y}^{2}}$ $V = sqrt(V_x^2+V_y^2)$

Thus,

$| P | = \sqrt{21^{2} + 6^{2}} \approx 21 c m$ $abs(P) = sqrt(21^2+6^2) approx 21cm$ , and

$| Q | = \sqrt{25^{2} + 9^{2}} \approx 27 c m$ $abs(Q) = sqrt(25^2+9^2) approx 27cm$

Recall that $- \to M$ $vec M$ is the sum of the preceding vectors,

$M_{x} = P_{x} + Q_{x} = 4 c m$ $M_x = P_x+Q_x = 4cm$ , and
$M_{y} = P_{x} + Q_{x} = 15 c m$ $M_y = P_x+Q_x = 15cm$

Therefore, the magnitude of the resultant vector $- \to M$ $vec M$ is,

$| M | = \sqrt{4^{2} + 15^{2}} \approx 16 c m$ $abs(M) = sqrt(4^2+15^2) approx 16cm$

Hence, I would wager that,

puu.sh

is a fairly accurate sketch of the vectors, color coded per the question's specifications.

I'm open to feedback if I made a mistake!

Answer 2 · 2018-01-18T19:46:58

$please review the details below.$ $"please review the details below."$

enter image source here

$P = \sqrt{{(- 21)}^{2} + 6^{2}} = \sqrt{441 + 36} = 21.84 cm$ $P=sqrt((-21)^2+6^2)=sqrt(441+36)=21.84" cm"$

enter image source here

$P = \sqrt{{(25)}^{2} + 9^{2}} = \sqrt{625 + 81} = 26.57 cm$ $P=sqrt((25)^2+9^2)=sqrt(625+81)=26.57 " cm"$

enter image source here

${- \to M}_{x} = {\to P}_{x} + {\to Q}_{x} = - 21 + 25 = + 4 cm$ $vec M_x=vec P_x+vec Q_x=-21+25=+4" cm"$

${- \to M}_{y} = {\to P}_{y} + {\to Q}_{y} = + 6 + 9 = + 15 cm$ $vec M_y=vec P_y+vec Q_y=+6+9=+15" cm"$

enter image source here

$M = \sqrt{4^{2} + 15^{2}} = \sqrt{16 + 225} = \sqrt{241} = 15.52 cm$ $M=sqrt(4^2+15^2)=sqrt(16+225)=sqrt(241)=15.52 " cm"$