Question
A running man has half the kinetic energy that a boy of half his mass has. The man speeds up by 1.0m/s and then has the same kinetic energy as the boy. What were original speed of man and boy?
Solution
Let M and m be the mass of man and boy respectively.
Let, the original velocities of man and boy be v1 and v2 respectively.
we have,
Mass of the boy is half of mass of man.
That is,
And K.E of the boy is equal to the K.E of man.
i.e.,
i.e.
...(1)
When the speed of man increases by 1m/s, the kinetic energies of both man and boy become same.
i.e.
...(2)
From eqn. (1) and (2),
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On solving we get,
Velocity of the man,
Velocity of the boy,
Let, the original velocities of man and boy be v1 and v2 respectively.
we have,
Mass of the boy is half of mass of man.
That is,
And K.E of the boy is equal to the K.E of man.
i.e.,
i.e.
...(1)When the speed of man increases by 1m/s, the kinetic energies of both man and boy become same.
i.e.
...(2)From eqn. (1) and (2),
On solving we get,
Velocity of the man,
Velocity of the boy,
