Question

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?

Answer 1

Let's provide several denotations:

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

We'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 ==> Mg*Vg = Pp ==> 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.