Question

A 20600 kg sailboat experiences an eastward force 17700 N due to the tide pushing its hullwhile the wind pushes the sails with a force of 60000 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 1

2.23 m/s²

Step-by-step explanation:

mass of sail boat, m = 20600 kg

Force along east, F1 = 17700 N

Force along north west, F2 = 60000 N

write the forces in vector form

`\overrightarrow{F_(1)}=17700 \widehat{i}`

`\overrightarrow{F_(2)}=60000\left ( - Cos45 \widehat{i}+Sin45\widehat{j}\right )`

`\overrightarrow{F_(2)}=-42426.41\widehat{i}+42426.41\widehat{j}`

Net force acting on the boat

`\overrightarrow{F}=\overrightarrow{F_(1)}+\overrightarrow{F_(2)}`

`\overrightarrow{F}=17573.6\widehat{i}+42426.41\widehat{j}`

The magnitude of net force is given by

`F=\sqrt{17573.6^(2)+42426.41^(2)}`

F = 45922 N

Acceleration = force / mass

a = 45922 / 20600

a = 2.23 m/s²