Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A river is flowing with a speed of
. A swimmer wants to go to point C starting from
A. He swims with a speed of
at an angle
w.r.t. the river flow. If AB
. Find the value of
.

Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Identify the parameters
Let the speed of the river be $v_r = 5 ext{ km/hr}$ and the speed of the swimmer be $v_s = 10 ext{ km/hr}$.
Step 2: Understand the swimming angle
The swimmer swims at an angle $\theta$ with respect to the upstream direction to compensate for the downstream flow of the river.
Step 3: Break down the swimmer's velocity
The horizontal (across the river) component of the swimmer's velocity is $v_s \cos(\theta)$ and the vertical component (against the river flow) is $v_s \sin(\theta)$.
Step 4: Set up the equation to reach point C
The horizontal component must equal the speed of the river to ensure that the swimmer reaches directly across to point C:
$$v_s \sin(\theta) = 5\text{ km/hr}$$
Step 5: Compute the time to swim from A to C
Distance from A to C is $BC = 400 ext{ m} = 0.4 ext{ km}$. Time taken can be determined as:
$$t = \frac{Distance}{Speed} = \frac{0.4}{v_s}$$
Step 6: Substitute the swimmer's speed
Thus, the time becomes:
$$t = \frac{0.4}{10 \sin(\theta)}$$
Step 7: Find the required angle
From the triangle formed by the current speed, swimmer's speed, and the resultant vector reaching point C, we can deduce that \( \sin(\theta) = \frac{v_r}{v_s} = \frac{5}{10} = 0.5 \) and hence $\theta = 30^\circ$.
Therefore, using the equation, with $\theta$ known, we can then compute the distance D = v_s x time = 5.
Step 8: Conclusion
Hence, the required value of D is 5.
Therefore, B.
Let the speed of the river be $v_r = 5 ext{ km/hr}$ and the speed of the swimmer be $v_s = 10 ext{ km/hr}$.
Step 2: Understand the swimming angle
The swimmer swims at an angle $\theta$ with respect to the upstream direction to compensate for the downstream flow of the river.
Step 3: Break down the swimmer's velocity
The horizontal (across the river) component of the swimmer's velocity is $v_s \cos(\theta)$ and the vertical component (against the river flow) is $v_s \sin(\theta)$.
Step 4: Set up the equation to reach point C
The horizontal component must equal the speed of the river to ensure that the swimmer reaches directly across to point C:
$$v_s \sin(\theta) = 5\text{ km/hr}$$
Step 5: Compute the time to swim from A to C
Distance from A to C is $BC = 400 ext{ m} = 0.4 ext{ km}$. Time taken can be determined as:
$$t = \frac{Distance}{Speed} = \frac{0.4}{v_s}$$
Step 6: Substitute the swimmer's speed
Thus, the time becomes:
$$t = \frac{0.4}{10 \sin(\theta)}$$
Step 7: Find the required angle
From the triangle formed by the current speed, swimmer's speed, and the resultant vector reaching point C, we can deduce that \( \sin(\theta) = \frac{v_r}{v_s} = \frac{5}{10} = 0.5 \) and hence $\theta = 30^\circ$.
Therefore, using the equation, with $\theta$ known, we can then compute the distance D = v_s x time = 5.
Step 8: Conclusion
Hence, the required value of D is 5.
Therefore, B.
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