A running man has half the kinetic energy of a boy half his mass. The man speeds up by 1.30 m/s and then has the same kinetic energy as the boy. What is the speed (in meters/second) of the boy?

Answer 1

man velocity: x
boy velocity: b
1/2 (2m)x^2 = 1/2 * 1/2 my^2
4x^2 = y^2

1/2 (2m)(x+1.3)^2 = 1/2 my^2
2(x+1.3)^2 = 4x^2
x^2 + 2.6x + 1.69 = 2x^2
x^2 - 2.6x - 1.69 = 0
x = 3.138

check:
1/2 (2m)*3.138^2 = 1/2 * 1/2 m*6.276^2
9.847 = 1/2 * 19.694 = 9.847

1/2 (2m)*4.438^2 = 1/2 m*6.276^2
19.694 = 19.694