Please Explain these 2 Momentum Physics Problems?

Question

please do these problems wih explanation !!!!
1. a 10g bullet, traveling at 400m/s hits a 2kg block of wood & emerges going at350m/s. How fast does the blck of wood move after being hit?

2. a child throws, at 10 m/s, a 3.4 kg package, horizontally, from a boat. The boat weighs 60 kg and the child weighs 20 kg. If the boat was initially at rest, what was it's speed after the throw ?

Answer 1

All these problems are solved by invoking the conservation of momentum law. Basically is says all the momentum before an impact equals all the momentum after an impact. It's that simple.

Momentum = P = mv; where m is the total mass moving with a net velocity of v. Thus, for 1:

mv = .01 kg X 400 m/sec = momentum before impact = momentum after impact = mv' + MV = .01 kg X 350 m/sec + 2.0 X V = the momentum of the bullet as it emerges plus the momentum of the block. Solving we have mv = mv' + MV; m(v - v') = MV; V = (m/M)(v - v') = (.01/2.0)(50)...you can do the math.

For 2:

mv = (M + c)V; where the LHS is the momentum of the throw of mass m = 3.4 kg at velocity v = 10 m/sec with the boat still and the RHS is the momentum of the boat and child (c = 20 kg) after the throw. Thus V = vm/(c + M) and you can do the math.

Lesson: momentum before an event (e.g., impact) is equal to momentum after that even due to the conservation of momentum.

Answer 2

All these questions are asking is how much energy is transferred into the said object, the bullet just can't lose momentum, it is transfered into the block of wood, the amount of energy lost is directly related to the mass of the block of wood. It is the same for the boat, the movement of the transfer from potential to kinetic energy is not just dispersed into the package, but also into the boat. Hope that helps you out, sorry I don't have any formulas.

Answer 3

There is a conservation of momentum-energy in the universe.
knowing that, you have:

momentum: p=m*v

1. a. pi=pf; with pi=(10*10^-3)*400, pf=(10*10^-3)*350+2*Vwood
now solve the equation

2. a. pi=pf; with pi=0, pf=(20+60)*Vboat+3.4*10 with Vboat<0 (in other direction), and assuming the child don't move (20(mass)*0 (v)).