Question:
A boat which has a speed of $5\, km/h$ in still water crosses a
river of width $1\, km$ along the shortest possible path in $15\, min$. The velocity of the river water in $km/h$ is
A boat which has a speed of $5\, km/h$ in still water crosses a
river of width $1\, km$ along the shortest possible path in $15\, min$. The velocity of the river water in $km/h$ is
Updated On: Jul 5, 2022
- 1
- 3
- 4
- $\sqrt {41}$
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The Correct Option is B
Solution and Explanation
Shortest possible path comes when absolute velocity of
boatman comes perpendicular to river current as shown in
figure.
$ \hspace20mm t = \frac{\omega}{v_b}=\frac{\omega}{\sqrt{v^2_{br}-v^2_r}}$
$\therefore \hspace15mm = \frac{1}{4}=\frac{1}{\sqrt{25-v^2_r}}$
Solving this equation, we get $v_r=3\, km/h$
$\therefore$ Correct answer is (b).
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Concepts Used:
Motion in a Plane
It is a vector quantity. A vector quantity is a quantity having both magnitude and direction. Speed is a scalar quantity and it is a quantity having a magnitude only. Motion in a plane is also known as motion in two dimensions.
Equations of Plane Motion
The equations of motion in a straight line are:
v=u+at
s=ut+½ at2
v2-u2=2as
Where,
- v = final velocity of the particle
- u = initial velocity of the particle
- s = displacement of the particle
- a = acceleration of the particle
- t = the time interval in which the particle is in consideration