Answer:
q is already given so i assume you question is find P
p = 187.6N
Explanation:
\widehat{p\ }+ \hat{q} = \hat{R}
R = 260N
q = 80N
angle between p and q is 30°
Therefore, the angle the two vectors make to produce R is (180° – 30° = 150°) = 150°
Resolving q in x and y components = (80 cos 30)i + (80 sin 30)j
q = 69.3i + 40j
R = p + q
Let p = xi + yj
R = (xi + yj) + (69.3i + 40j)
R = 260N
Resolving R in x and y components
R = (260 cos \theta)i + (260 sin \theta)j
(260 cos \theta)i + (260 sin \theta)j = (xi + yj) + (69.3i + 40j)
(260 cos \theta)i + (260 sin \theta)j = (x + 69.3)i + (y + 40)j
Equating each component to the corresponding component
x + 69.3 = (260 cos \theta)……(i)
y + 40 = (260 sin \theta)……….(ii)
y = 0
0+ 40 = (260 sin \theta)
\theta = sin-1 (\frac{40}{260})
\theta = 8.8°
x + 69.3 = 260 cos 8.8°
x = 260 cos 8.8° - 69.3
x = 187.6i
p = 187.6N
