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 ...

 

[thomate1]

For Question 1, you are correct in ruling out option a due to the loss of kinetic energy. Option b is also incorrect because the fragments can have different kinetic energies depending on their masses and velocities. Option c is incorrect because the sum of kinetic energies cannot be zero. Option e is also incorrect because the velocities of the fragments can be different. The correct answer is d, as momentum must be conserved in the explosion.

For Question 2, you are correct in choosing option c. This is because momentum must be conserved and the smaller fragment will have a larger velocity to compensate for its smaller mass.

For Question 3, you are correct in using the conservation of momentum equation, p = mv. You can use this to determine the final velocity and direction of Car 2 by setting the initial and final momenta equal to each other. You can then solve for the final velocity and use the direction of the final velocity to determine which arrow is correct.