$A$ ship is travelling due east at $10 \, km/hr$. $A$ second ship,heading $30^o$ east of north,is always due north of the first ship. The speed of the second ship in $km/hr$ is:

Rain is falling at an angle of $30^{\circ}$ from the vertical due to the wind with a speed of $40 \ m/s$. $A$ car is travelling horizontally in the direction opposite to the wind, at a speed of $40 \ m/s$. At what angle from the vertical will it experience the rain falling from (in $^{\circ}$)?

$A$ particle is moving along the $x$-axis with its coordinate with time '$t$' given by $x(t) = 10 + 8t - 3t^2$. Another particle is moving along the $y$-axis with its coordinate as a function of time given by $y(t) = 5 - 8t^3$. At $t = 1 \; s$,the speed of the second particle as measured in the frame of the first particle is given as $\sqrt{v}$. Then $v$ (in $m^2/s^2$) is:

$A$ man crosses a $320 \ m$ wide river perpendicular to the current in $4 \ minutes$. If in still water he can swim with a speed $5/3$ times that of the current,then the speed of the current,in $m/min$ is

$A$ boat having a speed of $5 \, km/hr$ in still water crosses a river of width $1 \, km$ along the shortest possible path in $15 \, minutes$. Find the speed of the river in $km/hr$.

$A$ moves with $65 \, km/h$ while $B$ is moving in the same direction as $A$ with $80 \, km/h$. The relative velocity of $B$ with respect to $A$ is ......... $km/h$.