The forces acting on a sailboat are 390 n north and 180 n east. if the boat (including crew) has a mass of 270 kg, what are the magnitude and direction of its acceleration?

(a) magnitude of acceleration:
we will imagine that the two components of the force are the sides of a right-angled triangle.
We can thus use the Pythagorean theorem to find the magnitude of the force which is the hypotenuses of this triangle
Magnitude of force = sqrt(390^2 + 180^2) = 429.53 Newton,
Using Newton's second law (F=ma), we can find the acceleration as follows:
429.53 = 270 * a 
a = 1.59 m/sec^2

(b) direction of acceleration:
we will again consider the right angled triangle formed from the components of the force.
Using the trigonometric function (tan = opposite / adjacent), we can find the direction of the force as follows:
tan theta = 390 / 180
tan theta = 2.1667
theta = 65.22 degrees 

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