The width of river is 1 km. The velocity of boat is 5 km/hr. The boat covered the width of river with shortest will possible path in 15 min. Then the velocity of river stream is:
The width of river is 1 km. The velocity of boat is 5 km/hr. The boat covered the width of river with shortest will possible path in 15 min. Then the velocity of river stream is:
\(3 \ km/hr\)
\(4 \ km/hr\)
\(\sqrt {29} \ km/hr\)
\(\sqrt {41} \ km/hr\)
The Correct Option is A
Solution and Explanation
\(t=\frac {d}{\sqrt {υ^2-v^2}}\)
\(\frac 14= \frac {1}{\sqrt {(5)^2-v^2}}\)
\(\frac {1}{16} = \frac {1}{25-v^2}\)
\(25-v^2 = 16\)
\(v^2 = 9\)
\(v =\sqrt {9}\)
\(v=3\ km/hr\)
So, the correct option is (A): \(3\ km/hr\)
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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