NEET Physics Two Dimensional Motion NEET PYQ-Two Dimensional Relative Motion

  • question_answer
    The speed of a boat is 5 km/h in still water. It crosses a river of width 1.0 km along the shortest possible path in 15 min. The velocity of the river water is: (in km/h) [AIPMT 1998]

    A) 5

    B) 1                     

    C) 3

    D) 4

    Correct Answer: C

    Solution :

    Let \[{{v}_{r}}=\] velocity of river
                \[{{v}_{br}}=\] velocity of boat in still water and
                \[w=\] width of river
                Time taken to cross the river\[=15\text{ }min\]
                Shortest path is taken when \[{{v}_{b}}\] is along AB. In this case
                Now,             \[t=\frac{w}{{{v}_{b}}}=\frac{w}{\sqrt{v_{br}^{2}-v_{r}^{2}}}\]
    \[\therefore \]      \[\frac{1}{4}=\frac{1}{\sqrt{{{5}^{2}}-v_{r}^{2}}}\]
    \[\Rightarrow \]   \[{{5}^{2}}-v_{r}^{2}=16\]
    \[\Rightarrow \]   \[v_{r}^{2}=25-16=9\]
    \[\therefore \]      \[{{v}_{r}}=\sqrt{9}\,=3\,km/h\]
    Note:    If \[{{v}_{r}}\ge {{v}_{br}},\] the boatman can never reach at point B.

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