A flag is mounted on a car moving due North with velocity of $20 \,\,km/hr$ Strong winds are blowing due East with velocity of $20\,\,km/hr$. The flag will point in direction

A river is flowing due east with a speed $3\, ms^{-1}$. A swimmer can swim in still water at a speed of $4\, ms^{-1}$ (figure).

$(a)$ If swimmer starts swimming due north, what will be his resultant velocity (magnitude and direction) ?

$(b)$ If he wants to start from point A on south bank and reach opposite point $B$ on north bank,

       $(i)$ Which direction should he swim ?
       $(ii)$ What will be his resultant speed ?

$(c)$ From two different cases as mentioned in $(a)$ and $(b)$ above, in which case will he reach opposite bank in shorter time ?

A fighter plane is flying horizontally at an altitude of $1.5\, km$ with speed $720\, km/h$. At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target ?

The $x$ and $y$ coordinates of the particle at any time are $x = 5t - 2t^2$ and $y = 10t$ respectively, where $x$ and $y$ are in metres and $t$ in seconds. The acceleration of the particle at $t = 2\, s$ is......$m/sec^2$

A vector has magnitude and direction. Does it have a location in space ? Can it vary with time ? Will two equal vectors $a$ and $b$ at different locations in space necessarily have identical physical effects ? Give examples in support of your answer.