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 ............ $\,m / s$

$Assertion$ : The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank may reach opposite bank simultaneously moving along different paths.
$Reason$ : For boats to cross the river in same time. The component of their velocity relative to river in direction normal to flow should be same.

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

Out of the two cars $A$ and $B$, car $A$ is moving towards east with a velocity of $10 \,m / s$ whereas $B$ is moving towards north with a velocity $20 \,m / s$, then velocity of A w.r.t. $B$ is ......... $m / s$ (nearly)

A boat is moving with velocity of $3\hat i + 4\hat j$ in river and water is moving with a velocity of $ - 3\hat i - 4\hat j$ with respect to ground. Relative velocity of boat with respect to water is :

The speed of a swimmer is $4\,km\,h ^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of river of width $1\,km$, he reaches a point $750 \,m$ down the stream on the opposite bank.The speed of the river water is $.........km h ^{-1}$