Question #20883

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?

Expert's answer

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

F2=87400 N

M=29000 kg

the angle between

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

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