Add the vectors: vector 1: 10m at 20 degrees N of E vector 2:10m at 80 degrees N of E x1= y1= x2= y2= x total= y total= magnitude of resultant= direction=

Question

asked Jul 14, 2021 24.2k views

1 Answer

Frantzy · Answer 1 · 2021-07-21T03:13:16+0000

Vector 1 has components

$x_1=(10\,\mathrm m)\cos20^\circ\approx9.40\,\mathrm m$

$y_1=(10\,\mathrm m)\sin20^\circ\approx3.42\,\mathrm m$

and vector 2 has

$x_2=(10\,\mathrm m)\cos80^\circ\approx1.74\,\mathrm m$

$y_2=(10\,\mathrm m)\sin80^\circ\approx9.85\,\mathrm m$

Add these vectors to get the resultant, which has components

$x_(\rm total)\approx11.133\,\mathrm m$

$y_(\rm total)\approx13.268\,\mathrm m$

The magnitude of the resultant is

$\sqrt{{x_(\rm total)}^2+{y_(\rm total)}^2}\approx17.321\,\mathrm m$

with direction
$\theta$ such that

$\tan\theta=(y_(\rm total))/(x_(\rm total))\implies\theta\approx50^\circ$

or about 50º N of E.