Question

A barge is pulled by two tugboats. The first tugboat is traveling at a speed of 12 knots with heading 140°, and the second tugboat is traveling at a speed of 17 knots with heading 200°. Find the resulting speed and direction of the barge. (Round your answers to the nearest whole number.) I got the speed but I don't know how to get the direction.

Answer 1

If you are using the parallelogram method where the resultant (r) is the diagonal, you should have
r^2 = 12^2 + 17^2 - 2(12)(17)cos 120°
= 637
r = √637 = appr 25.24 knots

let Ø be the angle between the resultant r and the first tug boat, then
sinØ/17 = sin120/25.24
I get Ø = 35.68°
so the bearing would be 140° + 35.68° = 175.68°
check my arithmetic

If you know vectors

then v1 = (12cos140, 12sin140) = (-9.1925, 7.7135)
v2 = (17cos200, 17sin200)= (-15.975 , -5.814)

resultant vector= v1+v2
= (-25.1673 , 1.8991)
r = √((-25.1673)^2 + 1.8991^2) = √637 = 24.24 as above
tanØ = 1.8991/-25.1673 = -.0075..
Ø = 180 - 4.315 = 175.68° as above