A person moves 30 m North and then 20 m towards East and finally $30 \sqrt{2} \mathrm{~m}$ in South-West direction. The displacement of the person from the origin will be

A river 200 m wide is flowing at a rate of $3.0 \mathrm{~m} / \mathrm{s}$. A boat is sailing at a velocity of $15 \mathrm{~m} / \mathrm{s}$ with respect to the water in a direction perpendicular to the river. How far from the point directly opposite to the starting point does the boat reach on the opposite bank?

Two cars $A$ and $B$ are moving with speeds $v_A=120 \mathrm{km} / \mathrm{h}$ and $v_B=50 \mathrm{~km} / \mathrm{h}$ respectively in the directions as indicated by the arrow in the figure below. What is the relative speed of the car $B$ with respect to car $A$ ?

Initial velocity with which a body is projected is $10 \mathrm{~m} / \mathrm{s}$ from the base of an inclined plane as shown in the given figure. If the angle of projection is $60^{\circ}$ with the horizontal, then the range $R$ is [take, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]