Question

A running man has the kinetic energy half that a boy of half his mass has. the man speeds up by 1.0 meter/sec and then has the same kinetic energy as the boy. what were the original speed of man and boy ?

• A. 2.4 m/sec , 4.8 m/sec
• B. 4.8 m/sec, 2.4 m/sec
• C. 4.2 m/sec, 8.4 m/sec
• D. 8.4 m/sec, 4.2 m/sec

Answer 1

The correct option is A 2.4 m/sec , 4.8 m/sec

Mass of Man $=M$

Velocity of man $=V_m$

Mass of Boy $=\frac{M}{2}$

Velocity of Boy $=V_B$

$\frac{1}{2}M{V}_m^2=\frac{1}{2}\left(\frac{1}{2}\frac{M}{2}{V}_B^2\right)$

$4V_m^2=V_B^2$

$2V_m=V_B.....\left(i\right)$

$\frac{1}{2}M(V_m+1{)}^2=\frac{1}{2}\frac{M}{2}{V}_B^2$

$(V_m+1{)}^2=\frac{1}{2}{V}_B^2$

From eq (i)

$(V_m+1{)}^2=2V_m^2$

$V_m=2.4m/s$

So $V_B=4.8m/s$

So, option (A)