Two forces of 16N and 8N are acting
simultaneously on a particle in
mutually perpendicular directions. Find
the magnitude and direction of the
resultant force.
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Answer:
The Resultant of vectors perpendicular to each other can be solved in two ways:
Method one: Pythagoras Theorem
a2 + b2 = c2
In the case of vectors c is replaced by the resultant R
a2 + b2 = R2
3^2 + 4^2 = R2
9 + 16 = R2
25 = R2
R = 5N
Method two: cosine rule
R2 = a2 + b2 + 2*a*b*cosα
Where R is resultant and α represents the angle between vectors a and b.
R2 = 3^2 + 4^2 + 2*3*4*cos90
R2 = 9 + 16 + 0
R2 = 25
Take the square root of both sides
R = 5N
For any other angle other than 90°, I suggest to use only the second method, the cosine rule.
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