Answer to Question #20883 in Mechanics | Relativity for ashley

Question

A 29000 kg sailboat experiences an eastward force 20600 N due to the tide pushing its hull while the wind pushes the sails with a force of 87400 N directed toward the northwest (45 westward of North or 45 northward of West). What is the magnitude of the resultant acceleration of the sailboat?

Answer 1

F1=20600 N
F2=87400 N
M=29000 kg
F_total=F1+F2
the angle between F1 and F2 is 135.
using the Law of cosines and the parallelogram law(rule):
F_total^2=F1^2+F2^2-2F1F2*cos(180-135)=F1^2+F2^2+2F1F2*cos(135)
a=F_total/M
a=Sqrt(F1^2+F2^2+2F1F2*cos(135))/M = 2.56m/s^2