A rowing boat of mass $120 \mathrm{kg}$ is being pulled from rest by three boats. One pulls north with a force of $100 \mathrm{N},$ the second pulls on a bearing of $020°$ with a force of $80 \mathrm{N}$ and the third pulls on a bearing of $045°$ with a force of $90 \mathrm{N}.$ There is resistance from the water of $200 \mathrm{N}$ directly against the motion. Find the bearing and acceleration of the resultant motion.

Three forces act on a particle in equilibrium in the horizontal plane, as shown in the diagram. Find the size of the unknown force $F$ and the angle $\theta .$

Three forces act on a particle in equilibrium in the horizontal plane, as shown in the diagram. By resolving in a direction perpendicular to $F,$ show that $\theta =47.2°$ and find $F.$

A boat is in equilibrium held by a rope to the shore. The rope exerts a force $T$ at an angle $\theta$ from north. The wind blows the boat with force $40 \mathrm{N}$ in a northwest direction. The current pushes it south with a force of $50 \mathrm{N}.$ Show that $T\sin \theta =20\sqrt{2}$ and find an expression for $T\cos \theta$. Hence, show that $\tan \theta =\frac{8+10\sqrt{2}}{17}$ and find $\theta$ and $T.$