A 2 000-kg sailboat experiences an eastward force of 3 000 N by the ocean tide and a wind force against its sails with magnitude of 6 000 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)30 $\degree$ N of W
C)30 $\degree$N of E
D)74 $\degree$ N of W

Question

Quizplus · Accepted Answer

First, we need to resolve the wind force into its components. Using trigonometry, we can find that the northward component is 4,243 N (6000 cos 45°) and the westward component is also 4,243 N (6000 sin 45°). 
Next, we can find the net force acting on the sailboat:
Net force = Eastward force - Westward force + Northward force
Net force = 3000 N - 4243 N + 0 N
Net force = -1243 N (directed westward) 
Finally, we can use Newton's second law (F = ma) to find the direction of the resultant acceleration:
Resultant acceleration = Net force / mass
Resultant acceleration = -1243 N / 2000 kg
Resultant acceleration = -0.62 m/s^2 (directed westward)
Therefore, the direction of the resultant acceleration is 74° west of north, which is answer choice D.

A 2 000-Kg Sailboat Experiences an Eastward Force of 3 °\degree°

A 2 000-Kg Sailboat Experiences an Eastward Force of 3 $\degree$