1. Given data

• Speed of river flow: $v_r = 2\ \text{km/h}$
• Speed of swimmer relative to water: $v_s = 4\ \text{km/h}$

We need the swimmer to cross the river straight, i.e. the resultant velocity must be perpendicular to the flow of the river.

2. Condition for straight crossing

Let the river flow along the positive $x$-direction. To cross straight, the swimmer’s resultant velocity should have zero component along the flow.

So, the swimmer must aim upstream such that the horizontal component of swimming velocity cancels the river speed.

If $\theta$ is the angle made by the swimmer’s direction with the flow of the river, then the component along the flow is:

$4\cos\theta$

Since this must oppose the river flow of $2\ \text{km/h}$,

$4\cos\theta = -2$

$\cos\theta = -\frac{1}{2}$

$\theta = 120^\circ$

3. Check

At $120^\circ$ with the flow:

• Horizontal component of swimmer’s velocity: $4\cos120^\circ = 4\left(-\frac{1}{2}\right) = -2$
• River flow component: $+2$

Net horizontal component:

$-2 + 2 = 0$

Hence, the swimmer moves straight across.

4. Option check

• A: $150^\circ$ $\rightarrow$ horizontal component too large upstream
• B: $120^\circ$ $\rightarrow$ correct
• C: $60^\circ$ $\rightarrow$ along the flow, not upstream
• D: $90^\circ$ $\rightarrow$ no upstream component, so drift occurs

Therefore, the correct option is B.