A running man has half the kinetic energy than a boy of half his mass has. The man speed up by 1.0 ms-1 and then he has the same energy as the boy. The original speeds of the man and boy respectively are

Question

A running man has half the kinetic energy than a boy of half his mass has. The man speed up by 1.0 ms-1 and then he has the same energy as the boy. The original speeds of the man and boy respectively are (A) 2.4 ms-1, 1.2 ms-1 (B) 1.2 ms-1, 4.4 ms-1 (C) 2.4 ms-1, 4.8 ms-1 (D) 4.8 ms-1, 2.4 ms-1

Tardigrade Admin · Accepted Answer

As the kinetic energy of the man is half the kinetic energy of the boy

∴ \frac{1}{2} M V^{2} = \frac{1}{2} (\frac{1}{2} m v^{2})

or

\frac{1}{2} M V^{2} = \frac{1}{2} \frac{1}{2} (\frac{M}{2}) v^{2} (∵ m = \frac{M}{2})

or

v^{2} = 4 V^{2}

or

v = 2 V

.
Here,

M

and

V

for man and

m

and

v

for boy.
Now when the velocity of the man is increased to

(V + 1)

, then kinetic energies become equal

\frac{1}{2} M (V + 1)^{2} = \frac{1}{2} (\frac{M}{2}) v^{2}

=

\frac{1}{4} M (2 V)^{2}

V^{2} + 2 V + 1 = 2 V^{2}

or

V^{2} - 2 V - 1 = 0

V = 2 + 1 = 2.4 m s^{- 1}

and

v = 2 (2 + 1) = 4.8 m s^{- 1}

.

Q. A running man has half the kinetic energy than a boy of half his mass has. The man speed up by $1.0 m s^{- 1}$ and then he has the same energy as the boy. The original speeds of the man and boy respectively are

$2.4 m s^{- 1}$ , $1.2 m s^{- 1}$

$1.2 m s^{- 1}$ , $4.4 m s^{- 1}$

$2.4 m s^{- 1}$ , $4.8 m s^{- 1}$

$4.8 m s^{- 1}$ , $2.4 m s^{- 1}$

Q. A running man has half the kinetic energy than a boy of half his mass has. The man speed up by 1.0ms−1 and then he has the same energy as the boy. The original speeds of the man and boy respectively are

2.4ms−1, 1.2ms−1

1.2ms−1, 4.4ms−1

2.4ms−1, 4.8ms−1

4.8ms−1, 2.4ms−1

Q. A running man has half the kinetic energy than a boy of half his mass has. The man speed up by $1.0 m s^{- 1}$ and then he has the same energy as the boy. The original speeds of the man and boy respectively are

$2.4 m s^{- 1}$ , $1.2 m s^{- 1}$

$1.2 m s^{- 1}$ , $4.4 m s^{- 1}$

$2.4 m s^{- 1}$ , $4.8 m s^{- 1}$

$4.8 m s^{- 1}$ , $2.4 m s^{- 1}$