How Is Momentum Conserved in Different Collision Scenarios?

[Nano]

Homework Statement

QUESTION 1 :A stationary bomb explodes in space breaking into a number of small fragments. At the location of the explosion, the net force do to gravity is 0 Newtons. Which one of the following statements concerning the event is true?
a) Kinetic energy is conserved in the process
b) The fragments must have equal kinetic energies
c) The sum of the KE's of the fragments must be 0
d) The vector sum of the linear momenta of the fragments must be zero
e) The velocity of anyone fragment must be equal to the velocity of any other fragment

QUESTION 2 : An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and 2m respectively. Which of the statements is true (after the explosion)?
a) They may fly off at right angles
b) They may fly off in the same direction
c) The smaller fragment will have twice the speed of the larger fragment
d) The larger fragment will have twice the speed of the smaller fragment
e) the smaller fragment will have four times the speed of the larger fragment

QUESTION 3: Car one is traveling due north and Car Two is traveling due east. After the collision shown, Car 1 rebounds due south. Which of the numbered arrows is the only one that can represent the final direction of Car 2.
Arrow 1 - 180 degrees
Arrow 2 - 150 degrees
Arrow 3 - 90 degrees
Arrow 4 - 30 degrees
Arrow 5 - 0 degrees

Homework Equations

p = mv
Impulse = force * time = change in momentum

The Attempt at a Solution

QUESTION 1 : Its obviously not an elastic collision because kinetic energy is lost in the explosion--which rules out a. Kinetic energy is always positive, so the sum can't be zero--not c. I don't understand b or e. I think its d, because momentum has to be conserved.
QUESTION 2 : I think its c, because momentum must be conserved and that is the only way that both fragments have a momentum of 2ms after the collision
QUESTION 3: I have no idea how to solve this problem. How can you find the direction of final velocity without pluggin in numbers?

 

[LowlyPion]

The first 2 look OK.

The third one, wants you to conserve momentum in both x and y.

Before the collision you had +Y and -X momentum, after you have some -Y and ...