Question

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 .

Answer 1

`2.95 m/s^(2)`

Step-by-step explanation:

The resultant force F

`F=\sqrt {F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)cos135^(o)}` where
`F_(1)` is eastward force,
`F_(2)` is force directed towards the North

`F=\sqrt {42700^(2)+85000^(2)+(2*42700*85000)cos135^(o)}=62573.17217 N`

F=62573.2 N

The magnitude of acceleration of sailboat is given by

`a=\frac {F}{m}=\frac {62573.2}{21200}=2.95 m/s^(2)`