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 magnitude of the resultant acceleration? A)2.2 m/s² B)2.1 m/s² C)1.5 m/s² D)3.0 m/s²

Question

Quizplus · Accepted Answer

We can break the wind force into its horizontal and vertical components as follows:
F_horizontal = 6000 cos 45° = 4243 N westward
F_vertical = 6000 sin 45° = 4243 N upward

Now, we can calculate the net force in each direction:

Net horizontal force = F_eastward + F_horizontal = 3000 N - 4243 N = -1243 N westward
Net vertical force = F_vertical = 4243 N upward

Next, we can use Newton's second law to calculate the acceleration:
a_horizontal = (Net horizontal force) / mass = (-1243 N) / 2000 kg = -0.62 m/s² westward
a_vertical = (Net vertical force) / mass = (4243 N) / 2000 kg = 2.12 m/s² upward

The magnitude of the resultant acceleration can be found using the Pythagorean theorem:
a_resultant = √(a_horizontal² + a_vertical²) = √((-0.62 m/s²)² + (2.12 m/s²)²) = 2.2 m/s²

Therefore, the answer is choice A, 2.2 m/s².

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

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