Question

A running man has half the kinetic energy that a
boy of half his mass has. The man speeds up by
1 m/s and then has the same kinetic energy as
the boy. What are the original speeds of the man
and the boy?​

Answer 1

Explanation:

let m1 be mass of man and m2 be mass of boy

then k1 = 1/2 m1(v1) ^2

k2 = 1/2 m2 (v2) ^2

given m2 = m1/2

then k2 = 1/4m1 (v2) ^2

if man increases by 1m/s speed then

kinetic energy is k3= 1/2 m1(v1 + 1)^2

given k1 = 1/2 k2 and k3= k2

from the above v1 = v2/2

k3= 1/2 m1(v2/2+1) ^2

as k3= 1/2 m1 { ((v2) ^2)/4+1 +v2}

as k3 = k2

by solving we get 1+ (v2) = (v2) ^2

2+2(v2) = (v2) ^2

v2= 1+√3

v1= v2/2

v1= (1+√3) /2