A man can swim at a speed of 5 km/h W.r.t water. He wants to cross a 1.5 km wide river flowing at 3 km/h. He keeps himself always at an angle of 60° with the flow of direction while swimming, The time taken by him to cross the river will be

Options

A. 0.26 hr
B. 0.35 hr
C. 0.45 hr
D. 0.55 hr

Answer

To solve the problem, we need to determine the time taken by the man to swim across the river while considering the river's current and his swimming angle. Here’s a step-by-step solution:

### Step 1: Understand the problem
The man swims at a speed of 5 km/h with respect to the water. The river flows at 3 km/h. He swims at an angle of 60° with respect to the direction of the river flow. The width of the river is 1.5 km.

### Step 2: Break down the swimming speed into components
Since the man swims at an angle, we need to find the vertical and horizontal components of his swimming speed.

- **Vertical component (V_vertical)**: This component will help him cross the river.
- **Horizontal component (V_horizontal)**: This component will be affected by the river's current.

Using trigonometry, we can find these components:
- Vertical component:
\[ V_{\text{vertical}} = V \cdot \cos(\theta) = 5 \cdot \cos(60°) = 5 \cdot \frac{1}{2} = 2.5 \text{ km/h} \]
- Horizontal component:
\[ V_{\text{horizontal}} = V \cdot \sin(\theta) = 5 \cdot \sin(60°) = 5 \cdot \frac{\sqrt{3}}{2} = \frac{5\sqrt{3}}{2} \text{ km/h} \]

### Step 3: Calculate the effective speed across the river
The effective speed across the river (the vertical component) is 2.5 km/h. The horizontal component will not affect the time taken to cross the river but will determine where he lands on the opposite bank.

### Step 4: Calculate the time taken to cross the river
To find the time taken to cross the river, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Here, the distance to cross is 1.5 km and the speed is the vertical component:
\[ \text{Time} = \frac{1.5 \text{ km}}{2.5 \text{ km/h}} = 0.6 \text{ hours} \]

### Step 5: Convert time into minutes
To convert hours into minutes, we multiply by 60:
\[ 0.6 \text{ hours} \times 60 \text{ minutes/hour} = 36 \text{ minutes} \]

### Final Answer
The time taken by the man to cross the river is **36 minutes**.

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