The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by :

CONCEPT:

Velocity: Velocity is defined as the speed of the object which is traveling from one place to another point with respect to time or we can say the ratio of displacement to the time taken by an object. Its S.I. unit is m/s.It is written as;

\(v =\frac{displacement}{time}=\frac{x}{t}\)

Here, x is the displacement, t is the time taken and v is the velocity.

CALCULATION:

Given: speed of still water, V_SR = 20 m/s

and the speed of river water, VRG = 10 m/s

When the swimmer is standing on the south bank and he wishes to cross the river along with the shortest path  as shown in the figure below,

Here we have to find the angle \(\theta\) at which he should make his strokes with respect to the north.

As we saw in the figure we have;

\({\vec V_{SG}} = {\vec V_{SR}} + {\vec V_{RG}}\)

As we know

 \(sin\theta=\frac{Perpendicular}{Hypotenuse}\)

⇒ \(\sin θ = \frac{{|{{\vec V}_{RG}}|}}{{|{{\vec V}_{SR}}|}}\) ----(1)

Now, on putting the values of speed in equation (1) we have;

\({\mathop{\rm sin}\nolimits} θ = \frac{{10}}{{20}}\)

⇒ \({\mathop{\rm sin}\nolimits} θ = \frac{{1}}{{2}}\)

⇒ θ = 30° West

Hence, Option 1) is the correct answer.