A stationary man observes that the rain is falling vertically downward. When he starts running with a velocity of $12\,\,km/h$ he observes that the rains is falling at an angle $60^o$ with the vertical. The actual velocity of rain is
$12\sqrt 3\,\,km/h$
$6\sqrt 3\,\,km/h$
$4\sqrt 3\,\,km/h$
$2\sqrt 3\,\,km/h$
A ship is travelling due east at $10\, km/hr$. $A$ ship heading $30^o$ east of north is always due north from the first ship. The speed of the second ship in $km/hr$ is
A boat is moving with a velocity $3i + 4j $ with respect to ground. The water in the river is moving with a velocity $-3i -4j $ with respect to ground. The relative velocity of the boat with respect to water is
A man can swim with a speed of $4.0\; km/h$ in still water. How long does he take to cross a river $1.0\; km$ wide if the river flows steadily at $3.0\; km/h$ and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank ?
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
A man standing on a road hold his umbrella at $30^° $ with the vertical to keep the rain away. He throws the umbrella and starts running at $10\, km/hr$. He finds that raindrops are hitting his head vertically, the speed of raindrops w.r.t. the moving man, will be