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A person of mass $M = 90\,kg$ standing on a smooth horizontal plane if ice throws a body of mass $m = 10\,kg$ horizontally on the same surface. If the distance between the person and body after $10\,\sec $ is $10\,m$, the $KE$ of the person (in joules) is:
(A) $0.45$
(B) $4.5$
(C) $0.90$
(D) zero

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Last updated date: 19th Apr 2024
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Answer
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Hint The kinetic energy can be determined by using the mass and the velocity of the person, the velocity of the person can be determined by using the distance and the time. The distance is determined by dividing the mass of the body by the total mass of the body and it is multiplied with the distance between the person and body.
Useful formula
The speed or the velocity of the person is given by,
$v = \dfrac{d}{t}$
Where, $v$ is the velocity of the person, $d$ is the distance of the person and $t$ is the time taken.
The kinetic energy of the person is given by,
$KE = \dfrac{1}{2}m{v^2}$
Where, $KE$ is the kinetic energy of the person, $m$ is the mass of the person and $v$ is the velocity of the person.

Complete step by step answer
The mass of the person is given as, $M = 90\,kg$,
The mass of the body is given as, $m = 10\,kg$,
The time taken is given as, $t = 10\,\sec $.
Now, the distance travelled by the person is equal to the dividing the mass of the body by the total mass of the body and it is multiplied with the distance between the person and body. Then,
$d = \dfrac{m}{{m + M}} \times 10\,m$
By substituting the mass of the person and the mass of the body in the above equation, then the above equation is written as,
$d = \dfrac{{10}}{{\left( {10 + 90} \right)}} \times 10\,m$
By adding the terms in the above equation, then the above equation is written as,
$d = \dfrac{{10}}{{100}} \times 10\,m$
By multiplying the terms in the above equation, then the above equation is written as,
$d = \dfrac{{100}}{{100}}\,m$
By dividing the terms in the above equation, then the above equation is written as,
$d = 1\,m$
Now,
The speed or the velocity of the person is given by,
$v = \dfrac{d}{t}$
By substituting the distance and the time taken in the above equation, then the above equation is written as,
$v = \dfrac{1}{{10}}$
By dividing the terms in the above equation, then the above equation is written as,
$v = 0.1\,m{s^{ - 1}}$
Now,
The kinetic energy of the person is given by,
$KE = \dfrac{1}{2}m{v^2}$
By substituting the mass of the person and the velocity of the person in the above equation, then the above equation is written as,
$KE = \dfrac{1}{2} \times 90 \times {\left( {0.1} \right)^2}$
By squaring the terms in the above equation, then the above equation is written as,
$KE = \dfrac{1}{2} \times 90 \times 0.01$
By multiplying the terms in the above equation, then the above equation is written as,
\[KE = \dfrac{1}{2} \times 0.9\]
By dividing the terms in the above equation, then the above equation is written as,
\[KE = 0.45\,J\]

Hence, the option (A) is the correct answer.

Note The velocity of the object is directly proportional to the distance and inversely proportional to the time. As the distance increases, then the velocity also increases. As the time increases, then the velocity decreases. The kinetic energy is directly proportional to the mass and the square of the velocity.