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° N of W).What is the magnitude of the resultant acceleration? A) 2.2 m/s² B) 2.4 m/s² C) 1.5 m/s² D) 3.0 m/s²

Question

Quizplus · Accepted Answer

First, we need to resolve the wind force vector into east and north components using trigonometry: 
North Force = 6000 N * sin(45°) = 4243 N 
East Force = 6000 N * cos(45°) = 4243 N 
Next, we can calculate the net force in the eastward direction: 
Net eastward force = 4243 N - 2000 N = 2243 N 
Then, we can calculate the net force in the northward direction: 
Net northward force = 4243 N 
Since there is no force acting in the upward or downward direction, we can use the Pythagorean theorem to find the magnitude of the resultant acceleration: 
Resultant acceleration = √[(2243 N)^2 + (4243 N)^2] / (2000 kg) = 2.4 m/s^2

A 2000-Kg Sailboat Experiences an Eastward Force of 2000 N