A boat has its motor running, creating a force of $500 \mathrm{N}.$ The wind is blowing it with a force of $200 \mathrm{N}.$ The directions of the forces are shown on the diagram. Find the direction of the subsequent motion.

A particle of mass $25 \mathrm{kg}$ has two forces acting on it, one of $20 \mathrm{N}$ and one of $35 \mathrm{N},$ in the directions shown. Find the magnitude and direction of the resulting acceleration.

Three coplanar forces act on a particle, as shown in the following diagram. $X$ has components $0 \mathrm{N}$ in the $x$ -direction and $20 \mathrm{N}$ in the $y$ -direction. $Y$ has components $25 \mathrm{N}$ in the $x$ -direction and $-10 \mathrm{N}$ in the $y$ -direction. $Z$ has components $-10 \mathrm{N}$ in the $x$ -direction and $-15 \mathrm{N}$ in the $y$ -direction. Find the magnitude and direction of the resultant of the three forces.

Four coplanar forces act on a particle, as shown in the following diagram. Show that the $x$ component and $y$ component of the resultant are equal. Hence, determine the direction of the resultant force.

In a competition of strength, four people pull a mass with ropes at different angles. The direction in which the mass moves determines the winner. Arjun wants the mass to go north, Bob wants it to go east, Chen wants it to go south and David wants it to go west. The men pull with the forces in the directions shown in the diagram. Find the direction of the resultant motion and determine who wins.