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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?

Respuesta :

Louli
(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 

[tex]\rm a = 1.59 \; m/sec^2[/tex]

[tex]\theta = 65.22^\circ[/tex]

Step by Step Solution :

Given :

Forces acting on a sailboat are 390N north and 180N east.

Mass = 270 kg

Calculation :

Resultant force is given by,

[tex]\rm F_R = \sqrt{390^2+180^2}[/tex]

[tex]\rm F_R = 429.53 \;N[/tex]

We know that

F = ma

[tex]429.53 = 270 \times a[/tex]

[tex]\rm a = 1.59 \; m/sec^2[/tex]

Therefore magnitude of acceleration is

[tex]\rm 1.59\; m/sec^2[/tex]

Now, for direction of acceleration

[tex]tan\theta = \dfrac{390}{180}=2.1667[/tex]

[tex]\theta = 65.22^\circ[/tex]

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https://brainly.com/question/16380983?referrer=searchResults

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