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# Answer to Question #6881 in Mechanics | Relativity for Misael

Question #6881
A 5-kg girl throws a 5.0-kg pumpkin at 10m.s to a 50-kg boy, who catches it. If both are on frictionless frozen lake, how fast does each of them move backward?
Let&#039;s provide several denotations:

Mg = 5 kg - girl&#039;s mass
Mp = 5 kg - pumpkin&#039;s mass
Mb = 50 kg - boy&#039;s mass
Vg - girl&#039;s velocity
Vp = 10 m/s - pumpkin&#039;s velocity
Vb - boy&#039;s velocity
Ig, Ip, Ib - girl&#039;s, pumpkin&#039;s and boy&#039;s momentum respectively

We&#039;ll use the the momentum conservation law:

Pp = Pg = Pb

We know that

Pp = Mp*Vp = 5kg*10m/s = 50 kg*m/s
Ig = Mg*Vg
Pb = Mb*Vb

So,

Pp = Pg ==&gt; Mg*Vg = Pp ==&gt; Vg = Pp/Mg = ( 50 kg*m/s ) / 5 kg = 10 m/s;
Analogically,
Vb = Pp/Mb = ( 50 kg*m/s ) / 50 kg = 1 m/s.

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