A 2000-kg sailboat experiences an eastward force of 2000 N by the ocean tide and a wind force against its sails with magnitude of 6000 N directed toward the northwest (45 $\degree$N of W). What is the direction of the resultant acceleration?
A) 60 $\degree$ N of E
B) 62 $\degree$N of W
C) 30 $\degree$N of E
D) 74 $\degree$N of W

Question

Quizplus · Accepted Answer

The resultant force is the vector sum of the eastward force and the northwest wind force. The eastward force is 2000 N, and the northwest force can be broken into components: 6000 N * cos(45°) westward and 6000 N * sin(45°) northward. The resultant force direction is determined by the arctan of the northward component over the net westward component, which results in approximately 62° N of W.

A 2000-Kg Sailboat Experiences an Eastward Force of 2000 N °\degree°

A 2000-Kg Sailboat Experiences an Eastward Force of 2000 N $\degree$