(B) Let $V_{sw} = 12 \, km/h$ be the velocity of the swimmer in still water and $v_r = 6 \, km/h$ be the velocity of the river flow.To reach the point

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(B) Let $V_{sw} = 12 \, km/h$ be the velocity of the swimmer in still water and $v_r = 6 \, km/h$ be the velocity of the river flow.To reach the point directly opposite to the starting point,the swimmer must swim at an angle $\theta$ with the normal to the river flow such that the component of his velocity cancels the river flow velocity.$V_{sw} \sin \theta = v_r$$12 \sin \theta = 6$$\sin \theta = \frac{6}{12} = \frac{1}{2}$$\theta = 30^{\circ}$ (angle with the normal).The angle $\alpha$ with respect to the direction of the river flow is given by $\alpha = 90^{\circ} + \theta = 90^{\circ} + 30^{\circ} = 120^{\circ}$.

Class 11 Physics 3-2.Motion in Plane Relative Velocity (river boat, rain, wind)

Difficult

$A$ swimmer can swim with a velocity of $12 \, km/h$ in still water. The water flowing in a river has a velocity of $6 \, km/h$. The angle with respect to the direction of flow of the river water at which the swimmer should swim in order to reach the point on the other bank just opposite to his starting point is ........$^{\circ}$. (Round off to the Nearest Integer)

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A
$30$
B
$120$
C
$60$
D
$150$

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3-2.Motion in Plane

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Relative Velocity (river boat, rain, wind)

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$A$ boat is sent across a river with a velocity of $8 \, km/hr$. If the resultant velocity of the boat is $10 \, km/hr$,then the velocity of the river is ........ $km/hr$.

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$A$ man walking along a straight line with a velocity $6 \text{ km/h}$ encounters rain falling vertically down with a velocity $6\sqrt{3} \text{ km/h}$. At what angle should the man hold his umbrella to protect himself from the rain?

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$A$ 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:

$A$ man standing on a road holds his umbrella at $30^\circ$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \, km/h$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the moving man will be:

$A$ boat is sent across a river with a velocity of $8 \, km/hr$. If the resultant velocity of the boat is $10 \, km/hr$,then the velocity of the river is ........ $km/hr$.

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