Physics help not answer please!?

Question

A child in a boat throws a 5.80 kg package out horizontally with a speed of 12.0 m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 27.0 kg and that of the boat is 45.0 kg.
Magnitude

Answer 1

No force external to the boat is acting so the momentum is conserved i.e. (27.0 + 45.0 )V= 5.80(12.0 )
V= 12(5.80)/72.0= 5.80/6 m/s

Answer 2

Hey ccg - the trick to this sort of question is remembering that some things in nature are conserved... four of them are momentum, mass-energy, charge, angular momentum. (There are others related to quantum mechanics, but they hardly matter in the real world we encounter.)

This means that if you impart momentum on something, that momentum has to come from you - so if you throw a stone, either you get pushed back, or the boat you're standing on does - or maybe just the earth gets pushed back. Something surely happens - it must.

So in your case, the package gets a momentum of mv = 5.8*12.0 kg m/s, so the child + boat must supply that momentum...

m_package*v_package + (M_boat + M_child) * V_boat ==0 (that's what conservation means - the changes add up to zip!)

You can re-arrange this and get how fast the boat recoils... actually, being a farm girl you've probably fired a rifle and will know all about recoil - it's exactly the same thing.

hth.
nj