Grade 11Vectors

the directions of 3 forces 10N,20N,30N acting at a point are parallel to the sides of an equilateral triangle taken in order. magnitude of their resultant is

Rajat Kashyap

8 Years agoGrade 11

2 Answers

Arun

8 Years ago

Forces A,B,C are 30N,20N,10N respectively. Let force A act along+ve x-axis then Force A = 30i Force B = (20cos120°)i + (20sin120°)j Force C= (10cos240°)i +(10sin240°)j So, Force A = 30i Force B= -10i +10√3j Force C= -5i -5√3j Resultant force(Position)=15i +5√3j Magnitude of resultant = 10√3 Direction of resultant = Resultant force vector/magnitude= (√3/2)i + (1/2)j

Amogh Vaishnav

7 Years ago

Let's put an x-axis on the direction of the 10N force
and a perpendicular y-axis.

The x-coord. of the resultant : 10 - 20cos60° - 30cos60° = -15
The y-coord. of the resultant : 20sin60° - 30sin60° = -5sqrt(3)
size of the resultant : sqrt(15² + 5²x3) = sqrt(300) = 10sqrt(3)