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A 21200 kg sailboat experiences an eastward force 42700 N due to the tide pushing its hull while the wind pushes the sails with a force of 85000 N directed toward the northwest (45◦ westward of North or 45◦ northward of West). What is the magnitude of the resultant acceleration of the sailboat? Answer in units of m/s 2 .

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opudodennis

Answer:

[tex]2.95 m/s^{2}[/tex]

Explanation:

The resultant force F

[tex]F=\sqrt {F_{1}^{2}+F_{2}^{2}+2F_{1}F_{2}cos135^{o}}[/tex] where [tex]F_{1}[/tex] is eastward force, [tex]F_{2}[/tex] is force directed towards the North

[tex]F=\sqrt {42700^{2}+85000^{2}+(2*42700*85000)cos135^{o}}=62573.17217 N[/tex]

F=62573.2 N

The magnitude of acceleration of sailboat is given by

[tex]a=\frac {F}{m}=\frac {62573.2}{21200}=2.95 m/s^{2}[/tex]

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