I need help finding the answer of this question using vector

37. A block and-tackle pulley hoist s sapended in a warchouse 37. A block-and-tackle pulley hoist is suspended in a warehouse by ropes of lengths 2 m and 3 m. The hoist weighs 350 N. The ropes, fastened at different heights, make angles of 50° and 38° with the horizontal. Find the tension in each rope and the magnitude of each tension. 38° 50° 3 m

Solution

Suppose tension in 2m rope is T2 and tension in 3m rope is T3.

system is in equilibrium hence Fnet = 0

in vertical,

T2sin50 + T3sin38 - W = 0

T2 sin50 + T3 sin38 = 350 .........(i)

IN horizontal,

T2cos50 - T3cos38 = 0

T2 = 1.226 T3

putting in (i),

(1.226T3)sin50 + T3 sin38 = 350

1.555 T3 = 350

T3 = 225.1 N ...........ans (Tension in right side 3 m rope)

T2 = 1.226T3 = 276 N .....Ans (Tension in left side 2m rope)