Vector Review Problem. Calculate the vector sum (i.e, the resultant ) for the fo

Question

Vector Review Problem. Calculate the vector sum (i.e, the resultant) for the following two velocity vectors: (12.0 m/s at 10.0°) + (7.00 m/s at 20.0°) The angles are given with respect to the positive x axis.
HINTS: You'll want to begin by calculating the x and y components of the two individual velocity vectors. Then answer the following questions about the resultant sum of the two vectors.

x component of the resultant:  m/s
y component of the resultant:  m/s

Magnitude of resultant (Units must be included):  

Direction:  °
Please find your angle by measuring in the counterclockwise direction from the positive x axis.

Explanation / Answer

A = 12cos(10) i + 12sin(10) j

B = 7cos(20) i + 7sin(20)j

A+B = (12cos(10)+7cos(20)) i +(12sin(10)+7sin(20))j

R = 18.4 i + 4.478 j

Rx = 18.4 m/s

Ry = 4.478 m/s

magnitude = (18.4^2 +4.478^2)^0.5

R = 18.94 m/s

direction:

theta = arctan(4.478/18.4)

theta = 13.7 degrees

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