Recoil velocity on frictionless surface

AI Thread Summary
The discussion focuses on calculating the recoil velocity of a child standing on frictionless ice after throwing a snowball. Participants explore the application of momentum and kinetic energy equations, noting that momentum conservation is applicable in this scenario while kinetic energy conservation may not be due to external energy input from the child. The importance of correctly applying the equations is emphasized, particularly in recognizing that kinetic energy is conserved in perfectly elastic collisions but not in inelastic ones. Clarification is sought on when to use the kinetic energy formula, with the consensus that it applies when no external forces affect the system. The conversation highlights the complexities of energy transfer in such scenarios.
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Homework Statement


A child stands on frictionless ice and throws a snowball. Estimate the recoil velocity of the child.

Homework Equations


m1v1i + m2v2i =m1v1 +m2v2f
1/2mv21i + 1/2 mv22i = 1/2 mv21f + 1/2mv22f

The Attempt at a Solution


After choosing estimates for weight of snowball, speed of child throwing snowball and weight of child I plugged it into the momentum and kinetic energy laws and solved for the final velocity in both of them, but I am not sure which equation is supposed to be used and in what situations
 
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Show your work in detail.
 
gneill said:
Show your work in detail.
Thanks, checked my work again and noticed i forgot to sq root for Vf in the KE formula, since it was negative only the momentum equation works. What type of questions would the KE formula be used though?
 
Kinetic energy is conserved when no external forces act on the system, or when there are no other avenues for energy loss or gain from the system. In perfectly elastic collisions kinetic energy is conserved. In inelastic collisions kinetic energy is not conserved.

A person throwing an object is equivalent to a "reverse" inelastic collision, where two bodies that were once connected are separated by some energy being injected: the person throwing the snowball is providing energy via their muscles, which is not accounted for by the simple conservation of KE formula applied to the individual masses.
 

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