Question:
A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is $0.5\, m/s$ at an angle of $120^?$ with the direction of flow of water. The speed of water is
A person swims in a river aiming to reach exactly on the opposite point on the bank of a river. His speed of swimming is $0.5\, m/s$ at an angle of $120^?$ with the direction of flow of water. The speed of water is
Updated On: Apr 15, 2024
- $1.0\, m/s$
- $0.5\, m/s$
- $0.25\, m/s$
- $0.43\, m/s$
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The Correct Option is C
Solution and Explanation
Let the speed of water $=\overrightarrow{u}$
Speed of swimmer $=\overrightarrow{v}=0.5\,m/sec$
Angle between $=\overrightarrow{v}$ and $=\overrightarrow{u}$ is $120^?$. Then
$sin\,\theta=\frac{\vec{u}}{\vec{v}} \Rightarrow \frac{u}{0.5}=\frac{1}{2} or u=0.25\,ms^{-1}$
Speed of swimmer $=\overrightarrow{v}=0.5\,m/sec$
Angle between $=\overrightarrow{v}$ and $=\overrightarrow{u}$ is $120^?$. Then
$sin\,\theta=\frac{\vec{u}}{\vec{v}} \Rightarrow \frac{u}{0.5}=\frac{1}{2} or u=0.25\,ms^{-1}$
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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