Find the direction and magnitude of the vectors. Part A Find the magnitude of th

ID: 2001101 • Letter: F

Question

Find the direction and magnitude of the vectors.

Part A
Find the magnitude of the vector A = (5.4 m )x + (1.5 m )y.

Part B
Find the direction of the vector A = (5.4 m )x + (1.5 m )y.
counterclockwise from the +x-axis

Part C
Find the magnitude of the vector B = (0.50 m )x + (5.4 m )y.

Part D
Find the direction of the vector B = (0.50 m )x + (5.4 m )y.
counterclockwise from the +x-axis

Part E
Find the magnitude of the vector A +B .

Part F
Find the direction of the vector A +B .
counterclockwise from the +x-axis

A.)

magnitude of the vector A = sqrt(5.4^2 + 1.5^2 )

=5.606

B.)direction of the vector A = tan-1(coefficient of y/ coefficient of x)

= tan-1(1.5 / 5.4) = 15.52o counterclockwise from the +x-axis

C.) magnitude of the vector B =sqrt( 0.5^2 + 5.4^2 )

= 5.423

D.) direction of the vector B = tan-1(coefficient of y/ coefficient of x) = tan-1(5.4/0.5) = 84.70ocounterclockwise from the +x-axis

E.) vector A +B . = (5.4 m )x + (1.5 m )y + (0.50 m )x + (5.4 m )y

= (5.9 m)x + (6.9 m) y

magnitude of the vector A +B .= sqrt((5.9 m)^2 + (6.9 m)^2 )

= 9.078 m

F.)direction of the vector A +B . = tan-1 (coefficient of y/ coefficient of x) = tan-1(6.9/5.9) =49.467o counterclockwise from the +x-axis

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