A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are _____ and _____ respectively.
Q. A river of width 200 m is flowing from west to east with a speed of 18 km/h. A boat, moving with speed of 36 km/h in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are _____ and _____ respectively.
A. 20 s and 100 m
B. 40 s and 100 m
C. 40 s and 200 m
D. 40 s and 0 m
Correct Answer: 40 s and 200 m

Explanation (Step-by-Step)

Convert speeds into m/s:

\[ 36 \text{ km/h} = 10 \text{ m/s} \]

\[ 18 \text{ km/h} = 5 \text{ m/s} \]

For minimum time, boat should move perpendicular to bank.

Effective velocity across river = 10 m/s

Time to cross one side:

\[ t_1 = \frac{200}{10} = 20 \text{ s} \]

Round trip time:

\[ t = 2 \times 20 = 40 \text{ s} \]

Drift during one crossing:

\[ \text{Drift} = 5 \times 20 = 100 \text{ m} \]

Total drift in round trip:

\[ 100 + 100 = 200 \text{ m} \]

Final Answer: 40 s and 200 m

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