A 66.0-kg boy and his 38.0-kg sister, both wearing roller blades, face each othe

Question

A 66.0-kg boy and his 38.0-kg sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity 3.30 m/s toward the west. Ignore friction. (a) Describe the subsequent motion of the girl. She will move east, directly away from her brother with a speed 7.38 m/s. She will move east, directly away from her brother with a speed 5.73 m/s. She will move east, directly away from her brother with a speed 1.65 m/s. She will move west, in the same direction as her brother, with a speed 3.30 m/s. (b) How much potential energy in the girl's body is converted into mechanical energy of the boy-girl system?

Explanation / Answer

Here ,

a) for the girl , let the velocity is vg

as there is no external force acting on the system

the momentum of the system will remain constant

66 * 3.3 + 38 * vg = 0

vg = -5.73 m/s

hence , She will move east directly away from high brother with a speed 5.73 m/s

b)

energy converted to mechanical energy = total kinetic energy of both

energy converted to mechanical energy = 0.50 * 66 * 3.3^2 + 0.50 * 38 * 5.73^2

energy converted to mechanical energy = 983.19 J

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