Distance vs Displacement in 2D

Q. A sailboat sails $2.0\text{km}$ east, then $4.0\text{km}$ southeast, then an additional distance in an unknown direction. Its final position is $5.0\text{km}$ directly east of the starting point. Find the magnitude and direction of the third leg of the journey. (Given, $2\sqrt{2}=2.83$)

1. $0.17\text{km},{\tan }^{-1}\left(16.65\right)$ East of North
2. $4\text{km},{\tan }^{-1}\left(16.65\right)$ East of North
3. $2.84\text{km},{\tan }^{-1}\left(16.65\right)$ North of East
4. $1\text{km},{\tan }^{-1}\left(1\right)$ North of East

Q. In a semicircular path of radius R unit, two points A and B are lies on diametrically opposite points. If a particle moves from A to B along the semicircular path, then what will be the displacement of the particle.

1. 4R unit
2. R unit
3. 3R unit
4. 2R unit

Q. A farmer moves along the boundary of the square field of side $10\text{m}$ in $40\text{seconds}$. What will be the magnitude of displacement of the farmer at the end of $2\text{minutes}20\text{seconds}$ from its initial position if he starts from one of the corners.

1. $0\text{m}$
2. $14.1\text{m}$
3. $30\text{m}$
4. $20\text{m}$

Q. A circle of radius $r$ moves forward on the ground and completes a full revolution. Find the final position of the centre of the circle after the revolution.

1. $0\hat{i}+r\hat{j}$
2. $2\pi r\hat{i}+r\hat{j}$
3. $\pi r^2\hat{i}+r\hat{j}$
4. $r\hat{i}+2\pi r\hat{j}$