Question

Two forces act on an object. The first Force has a magnitude of 400 Newtons and acts at an angle of 30 degrees as measured from the horizontal. Second Force has a magnitude of 280 Newtons in accident angle of 135 degrees is measured from the horizontal. Determine the vector v that represents the resultant Force.
a. v=(200-140rtsq2)i+(200rtsq3+140rtsq2)j
b. v=(200+140rtsq2)i+(200rtsq3+140rtsq2)j
c. v=(200rtsq3+140rtsq2)i+(200+140rtsq2)j
d. v=(200rtsq3-140rtsq2)i+(200+140rtsq2)j

Answer 1

ANSWER

Option D is correct

EXPLANATION

We resolve the forces into component forms.

$F_1 = 400 \cos(30) i + 400 \sin(30) j$

$F_1 = 200 \sqrt{3} i +200j$

Also the second is resolved to obtain,

$F_2= 280 \cos(135) i + 280 \sin(135) j.$

$F_2= - 140 \sqrt{2} i + 140 \sqrt{2} j$

To find the resultant vector, V, We add the corresponding components of the two forces to get:

$V=F_1+F_2$

$\implies \: V = (200 \sqrt{3} - 140 \sqrt{2} )i + (200 + 140 \sqrt{2})j$

The correct answer is D.