Answer to Question #2653 in Mechanics | Relativity for tom

Question

A vector C = [ 10 m , 30 degree ] and vector D = [ 25 m , 130 degree ]
Use the algebraic ( components) method to find the magnitude and direction of the sum R = C + D ?

Answer 1

The angle between the given vectors is 130-30 = 100 degree. From the Law of cosines the magnitude is
R² = 10² + 25² - 2*10*25*cos (100) = 811.82 m²
R = 28.5 m
Using the law of Sinuses we can find the angle between R and C:
28.5/sin100 = 25/sinx , sinx = 0.86, x = 60 degrees.
Thus the direction of the vector R is 180-60 + 30 = 150 degree.
Answer: 28.5 m, 150 degree.