Question

38. Two forces of magnitude 10 N and 20 N act on a body in directions
making angles 30° and 60° respectively with x-axis. What is the
resultant force?
A.
B.
C.
D.
17 N
19 N
23 N
29 N
37 N
E.​

Answer 1

Explanation:

Two forces of magnitude F1= 10N and F2 =20N act on a body in a direction making angle a = 30 and b = 60 degrees respectively with the x-axis. Thus the resultant force Fr acting on the body is given by,

Fr = i (F1 cos a + F2 cos b) + j ( F1 sin a + F2 sin b)

= i ( 10 cos 30 + 20 cos 60) + j ( 10 sin 30 + 20 sin 60).

= i { 10 x (√3/2) + (20 /2)} + j { (10/2)+ 20 x(√3/2)}

= i (5 √3 + 10) + j (5 + 10√3) N

I hope it helps you...