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 $\to O A, \to B C$ and $\to D E$ .

Open in App

Solution

X and Y components of all the forces given
x component of $\to O A$ = 2 cos $30^{0} = \sqrt{3}$

x component of $\to B C$ = 1.5 cos $120^{0}$ = $\frac{(1.5)}{2} = - 7.5$

x component of $\to D E$ = 1 cos $270^{0}$ = $1 \times 0 = 0$

y component of $\to O A = 2$ sin $30^{0} = 1$

y component of $\to B C$ = 1.5 sin $30^{0} = 120^{0}$ = $\frac{(\sqrt{3} \times 1.5)}{2} = 1.3$

y component of $\to D E$ = 1 sin $270^{0} = - 1$

x component of resultant,

$R_{x} = \sqrt{3}$ - 0.75+0

= 0.98 m

Resultant y component,

$R_{y}$ = 1+1.3-1 = 1.3 m

$∴$ Resultant, R = $\sqrt{(0.98)^{2} + (1.3)^{2}}$

= $\sqrt{0.96 + 1.69}$

= $\sqrt{2.65}$

= 1.6 m
The magnitude of the resultant of the given displacement is 1.6 m
Angle made with X-axis

If it makes an angle $α$ with +ve x axis, then

tan $α$ = $\frac{y component}{x component}$

= $\frac{1.3}{0.98} = 1.332$

$\Rightarrow α = t a n^{- 1} (1.32)$

Suggest Corrections

158

Similar questions

Q. Refer to figure (2-E1). Find (a) the magnitude, (b) x and y component and (c) the angle with the X-axis of the resultant of

\vec{OA}, \vec{BC} and \vec{DE}

Figure (2-E1)

Q. There are two forces each of magnitude 10 units. One inclined at an angle of

30^{0}

and the other at an angle of

135^{0}

to the positive direction of x-axis. The x and y components of the resultant are respectively.

Vector A has a magnitude of 2 units and makes an angle of $0^{\circ}$ with the positive x- axis, Vector B has a magnitude of 6 units and makes an angle of $30^{\circ}$
(clock-wise) with the positive y- axis. Find the magnitude of the resultant of Vector A& B and also the angle that it makes with Vector A.

Vector A has magnitude of 3 units and makes an angle of $30^{\circ}$ with the positive x-axis.

Vector B has magnitude of 4 units and makes an angle of $120^{\circ}$ with the positive x-axis.

Find the magnitude of the resultant and the angle that it makes with the positive x-axis.

$[t a n^{- 1} (\frac{4}{3}) = 53^{\circ}]$

Q. A vector of magnitude 10 has its rectangular component as as 8 and 6 along x axis and y axis respectively. Find the angles it make with the x and y axis?

Join BYJU'S Learning Program

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,→BC and →DE.

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 $\to O A, \to B C$ and $\to D E$ .