Question:
A man can swim with a speed of $4\,km\,h^{-1}$ in still water. He crosses a river $1\,km$ wide that flows steadily at $3\,km\,h^{-1}$. If he makes his strokes normal to the river current, how far down the river does he go when he reaches the other bank?
A man can swim with a speed of $4\,km\,h^{-1}$ in still water. He crosses a river $1\,km$ wide that flows steadily at $3\,km\,h^{-1}$. If he makes his strokes normal to the river current, how far down the river does he go when he reaches the other bank?
Updated On: Jul 5, 2022
- $500\,m$
- $600\,m$
- $750\,m$
- $850\,m$
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The Correct Option is C
Solution and Explanation
Time to cross the river,
$t=\frac{\text{Width of river}}{\text{Speed of man}}$
$=\frac{1\,km}{4\,km\,h^{-1}}$
$=\frac{1}{4}h$
Distance moved along the river in time $t$,
$s=v_{r}\times t=3\,km\,h^{-1}\times\frac{1}{4}h=\frac{3}{4}km$
$=750\,m$
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Notes on Motion in a plane
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