A 65kg boy and his 40kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backwards with a velocity of 2.9m/s towards the west. Ignore friction. What is the minimum amount of chemical energy is converted into mechanical energy in the girl’s muscles?

Answer 1

It is easy to calculate how much kinetic energy must be given to both brother and sister. The girl acquires an equal momentum in the opposite direction, with velocity 2.9*64/40 = 4.64 m/s.

Calculate and add the kinetic energies of both brother and sister.

Chemical (food) energy cannot be converted to mechanical energy with 100% efficiency. The efficiency varies from person to person, but is around 20%. They may want you to assume 100% efficiency for the minimum food energy required, but the real number is much higher.