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JEE Main 2024 · Physics · Kinematics and Laws of Motion · medium

A boat can move at 5 m s^-1 relative to still water. It crosses a river 120 m wide that flows at 3 m s^-1. The crossing time when the boat is steered…

Single correct option

A boat can move at 5 m s−15\ \mathrm{m\,s^{-1}} relative to still water. It crosses a river 120 m120\ \mathrm{m} wide that flows at 3 m s−13\ \mathrm{m\,s^{-1}}. The crossing time when the boat is steered to land at the point directly opposite the start, exceeds the minimum possible crossing time by
  1. A. 6 s6\ \mathrm{s}
  2. B. 8 s8\ \mathrm{s}
  3. C. 10 s10\ \mathrm{s}
  4. D. 4 s4\ \mathrm{s}
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Answer: (A) 6 s6\ \mathrm{s}

Minimum time: head perpendicular to the banks, tmin=120/5=24 st_{min}=120/5=24\ \mathrm{s}. To land directly opposite, the boat must cancel the drift: 5sin⁡θ=35\sin\theta=3, so the cross-stream component of velocity is 52−32=4 m s−1\sqrt{5^2-3^2}=4\ \mathrm{m\,s^{-1}} and t=120/4=30 st=120/4=30\ \mathrm{s}. Difference =30−24=6 s=30-24=6\ \mathrm{s}. A common slip is using 5−3=25-3=2 or 5+35+3 as the cross velocity.
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