Question:
Boat speed \(=5\ \text{m/s}\), river speed \(=3\ \text{m/s}\), width \(=40\ \text{m}\). Minimum time?
Boat speed \(=5\ \text{m/s}\), river speed \(=3\ \text{m/s}\), width \(=40\ \text{m}\). Minimum time?
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For minimum time to cross a river, point the boat perpendicular to the bank. The river current affects drift, not the crossing time.
Updated On: Jun 3, 2026
- \(5\ \text{s}\)
- \(8\ \text{s}\)
- \(10\ \text{s}\)
- \(20\ \text{s}\)
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The Correct Option is B
Solution and Explanation
Concept:
For crossing a river in minimum time, the boat should be directed perpendicular to the river flow. In minimum-time crossing, only the velocity component of the boat perpendicular to the river bank is used for crossing the width. So, \(\displaystyle \text{Minimum time}=\frac{\text{Width of river}}{\text{Speed of boat in still water}}\)
Step 1: Write the given values.
Speed of boat in still water: \(\displaystyle v_b=5\ \text{m/s}\) Speed of river: \(\displaystyle v_r=3\ \text{m/s}\) Width of river: \(\displaystyle d=40\ \text{m}\)
Step 2: Understand the role of river speed.
For minimum time, the boat is aimed straight across the river. The river current only causes drift downstream. It does not affect the time needed to cross the width. Therefore, for minimum time, we use only: \(\displaystyle v_b=5\ \text{m/s}\)
Step 3: Apply the formula.
\(\displaystyle t_{\min}=\frac{d}{v_b}\) \(\displaystyle t_{\min}=\frac{40}{5}\) \(\displaystyle t_{\min}=8\ \text{s}\)
Step 4: Final conclusion.
Hence, the minimum time required is: \(\displaystyle \boxed{8\ \text{s}}\)
For crossing a river in minimum time, the boat should be directed perpendicular to the river flow. In minimum-time crossing, only the velocity component of the boat perpendicular to the river bank is used for crossing the width. So, \(\displaystyle \text{Minimum time}=\frac{\text{Width of river}}{\text{Speed of boat in still water}}\)
Step 1: Write the given values.
Speed of boat in still water: \(\displaystyle v_b=5\ \text{m/s}\) Speed of river: \(\displaystyle v_r=3\ \text{m/s}\) Width of river: \(\displaystyle d=40\ \text{m}\)
Step 2: Understand the role of river speed.
For minimum time, the boat is aimed straight across the river. The river current only causes drift downstream. It does not affect the time needed to cross the width. Therefore, for minimum time, we use only: \(\displaystyle v_b=5\ \text{m/s}\)
Step 3: Apply the formula.
\(\displaystyle t_{\min}=\frac{d}{v_b}\) \(\displaystyle t_{\min}=\frac{40}{5}\) \(\displaystyle t_{\min}=8\ \text{s}\)
Step 4: Final conclusion.
Hence, the minimum time required is: \(\displaystyle \boxed{8\ \text{s}}\)
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