A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1 m/s so as to have same K.E. as that of the boy. The original speed of the man will be
Kinetic energy is defined as the half of the product of mass and square times the velocity. K.E=‌
1
2
Mv2,K.E where is the kinetic energy, M is the mass and v is the velocity of the object whose kinetic energy We are calculating.
First Case: The kinetic energy of the man is half the kinetic energy of the boy with half the mass. The man has a mass M and velocity v1 whereas the boy has mass ‌
M
2
and velocity v2 . ‌
1
2
Mv12=‌
1
2
(‌
1
2
‌
M
2
v22) v12=‌
1
4
(v22)
Second Case: The kinetic energy of the man is equal to the kinetic energy of the boy with half the mass. The man has a mass M and velocity v1+1 whereas the boy has mass ‌
M
2
and velocity v2. ‌
1
2
M(v1+1)2=‌
1
2
‌
M
2
v22 (v1+1)2=‌
1
2
v22 By taking the ratio both these relations we get ‌