A boy is moving with a constant speed $v$ on a small trolley towards a distant circle as shown in the figure. A point mass is moving on the circle with a constant speed $v$, what is the frequency of change in magnitude of relative velocity of the point mass, as observed by the boy.
$\frac{v}{{4R}}$
$\frac{v}{{2\pi R}}$
$\frac{v}{{4\pi R}}$
$\frac{v}{{\pi R}}$
The trajectory of a particle moving in vast maidan is as shown in the figure. The coordinates of a position A are $(0,2)$. The coordinates of another point at which the instantaneous velocity is same as the average velocity between the points are
A particle has initial velocity $\left( {2\hat i + 3\hat j} \right)$ and acceleration $\left( {0.3\hat i + 0.2\hat j} \right)$. The magnitude of velocity after $10\, seconds$ will be
and direction of the vectors $\hat{ i }+\hat{ j }$, and $\hat{ i }-\hat{ j }$ ? What are the components of a vector $A =2 \hat{ i }+3 \hat{ j }$ along the directions of $\hat{ i }+\hat{ j }$ and $\hat{ i }-\hat{ j } ?$
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 ?