What is the magnitude (to the nearest kilogram) and the direction angle (to the nearest tenth of a degree) of the resulting force?

Question

The magnitude and direction exerted by two tugboats towing a ship are 1800 kilograms, S82°E, and 1500 kilograms, N78°E, respectively. Find the magnitude, to the nearest kilogram, and the direction angle, to the nearest tenth of a degree, of the resulting force. Write the angle in the form of a heading, as shown for the tugboats in this problem.

Answer 1

S82^OE is 82 degrees east of due south. That is also -8^O.

N78^OE is 78 degrees east of due north. That is also 12^O.

So there is a 20 degree angle between these two directions.

Decompose the vectors into x and y components, and then add the vector components:

X = 1800*cos(-8) + 1500*cos(12)

Y = 1800*sin(-8) + 1500*sin(12)

Then use M = √[X² +Y²] to find the magnitude of the resultant force.

The direction can be found with this equation:

tan(A) = 1500*sin(20)/(1800+1500*cos(20))

Add the original -8 degrees, then convert to a heading.

If you will complete the calculations above, I will be glad to check them for you.

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Another method of determining the resultant angle is to compute:

tan^-1(Y/X)

with X and Y as defined above. Then convert the angle to a heading.