A swimmer can swim in still water with speed $v$ and the river is flowing with velocity $v/2$. To cross the river in shortest distance, he should swim making angle $\theta$ with the upstream. What is the ratio of the time taken to swim across the shortest time to that is swimming across over shortest distance
$cos \,\theta$
$sin \,\theta$
$tan\,\theta$
$cot \,\theta$
A man is running at a speed of $5\, m/s$, the rain drops appear to be falling at an angle of $45^o$ from the vertical. If the rain drops are actually falling vertically downwards, then velocity of rain drops (in $m/s$) is
An airplane airspeed indicator reads $100 \,m / s$ and its compass shows that it is heading $37^{\circ}$ east of north. The meteorological information provided to the navigator is that the wind velocity is $20 \,m / s$ towards east. The speed of the airplane relative to the ground is closest to ............ $\,m / s$
A river is flowing from east to west at a speed of $5\, m/min$ A man on south bank of river, capable of swimming $10\,m/min$ in still water, wants to swim across the river in shortest time. He should swim
A boat takes two hours to travel $8 \,km$ and back in still water. If the velocity of water is $4\, km/h$, the time taken for going upstream $8 \,km$ and coming back is
A man is crossing a river flowing with velocity of $5\,\, m/s$. He reaches a point directly across at a distance of $60\,\, m$ in $5 \,\,sec$. His velocity in still water should be ........ $m/s$