A body moves due East with velocity $20\, km/hour$ and then due North with velocity $15 \,km/hour$. The resultant velocity..........$km/hour$

A passenger arriving in a new town wishes to go from the station to a hotel located $10 \;km$ away on a straight road from the station. A dishonest cabman takes him along a circuitous path $23\; km$ long and reaches the hotel in $28 \;min$. What is

$(a)$ the average speed of the taxi,

$(b)$ the magnitude of average velocity ? Are the two equal ?

The five sides of a regular pentagon are represented by vectors $A _1, A _2, A _3, A _4$ and $A _5$, in cyclic order as shown below. Corresponding vertices are represented by $B _1, B _2, B _3, B _4$ and $B _5$, drawn from the centre of the pentagon.Then, $B _2+ B _3+ B _4+ B _5$ is equal to

Give the names of two methods for vector addition. Write the law of parallogram for vector addition.

Find the resultant of three vectors $\overrightarrow {OA} ,\,\overrightarrow {OB} $ and $\overrightarrow {OC} $ shown in the following figure. Radius of the circle is $R$.

Two forces of $10 \,N$ and $6 \,N$ act upon a body. The direction of the forces are unknown. The resultant force on the body may be .........$N$