JEE Main 2021 · Physics · Kinematics and Laws of Motion · medium

A boat has speed 5 m s^-1 relative to water in a river of width 120 m flowing at 3 m s^-1. Let t1 be the time to reach the point directly opposite…

Numerical answer

A boat has speed

5\ \mathrm{m\,s^{-1}}

relative to water in a river of width

120\ \mathrm{m}

flowing at

3\ \mathrm{m\,s^{-1}}

. Let

t_1

be the time to reach the point directly opposite the starting point, and

t_2

the minimum time to cross. The value of

t_1-t_2

in seconds is

Show answer and solution

Answer: 6

To land directly opposite, the boat must cancel the drift: effective cross speed

=\sqrt{5^2-3^2}=4\ \mathrm{m\,s^{-1}}

, so

t_1=120/4=30\ \mathrm{s}

. Minimum crossing time is with the heading perpendicular to the banks:

t_2=120/5=24\ \mathrm{s}

. Therefore

t_1-t_2=6\ \mathrm{s}

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