Question

Refer to figure (2-E1). Find

(a) the magnitude,
(b) x and y components and
(c) the angle with the x-axis of the resultant of OA vector , BC vector and DE vector.

Answer 1

Thanks for asking the question!

SOLUTION::

y component of OA vector = 2 sin 30° = 1 m
y component of BC vector = 1.5 sin 120° = 1.3 m
y component of DE vector = 1 sin 270° = -1 m

Resultant of y component = (1+ 1.3 - 1) m = 1.3 m

x component of OA vector = 2 cos 30° = √3 m
x component of BC vector = 1.5 cos 120° = - 0.75 m
x component of DE vector = 1 cos 270° = 0 m

Resultant of x component = (√3-0.75+0) m= (1.73 -0.75) m = 0.98 m

Total resultant of x and y component = √[(1.3)²+(0.98)²] = 1.6 m

Now,tan T = (y component/x component) = 1.32
T = tan⁻¹(1.32)
So, the resultant is 1.6 m and tan⁻¹(1.32) with positive x-axis.

Hope it helps!

Answer 2

Solution is provided in the given attachments .