Momentum of two balls collision question

In summary, two balls of equal mass m undergo a collision with one ball initially stationary. The velocities of the balls make angles of 33° and 43° relative to the original direction of motion of the moving ball. If the initial speed of the moving ball is 5.4 m/s, the final speed can be solved using two equations and two unknowns. By expressing V1' in terms of V2' and substituting into the second equation, the final speed can be solved.
  • #1
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Two balls of equal mass m undergo a collision. One ball is initially stationary. After the collision, the velocities of the balls make angles of 33° and 43° relative to the original direction of motion of the moving ball. If initial speed of moving ball is 5.4 m/s find the final speed.

What I've done:
In x axis:
M1V1+ M2V2= M1V1’+ M2V2’
M(5.4)+M(0)=M(V1’Cos33)+M(V2’Cos46)
5.4M= M( V1’Cos33+ V2’Cos46)
5.4= V1’Cos33+ V2’Cos46

In the y axis:
0= M1V1’+ M2V2’
0=M(V1’Sin33)-M(V2’Sin46)
(Dividing both sides by M)
0=( V1’Sin 33- V2’Sin46)
0= V1’Sin33- V2’Sin46i don't know what do do after this! please help!

HERES IMAGE OF PROBLEM WITH DIAGRAM:
http://i.imgur.com/NKSeA.jpg
 
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  • #2
You have two equations and two unknowns. Solve them simultaneously. Try using the method of substitution. (Use one equation to express V1' in terms of V2'. Then substitute that into the second equation and solve for V2'.)
 
  • #3
Doc Al said:
You have two equations and two unknowns. Solve them simultaneously. Try using the method of substitution. (Use one equation to express V1' in terms of V2'. Then substitute that into the second equation and solve for V2'.)

OMG THANKS YOU SO MUCH I DID IT RIGHT ON MY TEST!
PRETTY INTENSE BUT THANKS SO MUCH!
i found easier to use a,b for v1' and v2' made my life a lot easier
 

FAQ: Momentum of two balls collision question

What is momentum in a collision?

Momentum in a collision is the product of an object's mass and velocity. It is a measure of the object's motion and its resistance to changes in motion.

How is momentum conserved in a collision?

In a closed system, the total momentum before a collision is equal to the total momentum after the collision. This is known as the law of conservation of momentum.

What is an elastic collision?

An elastic collision is a collision in which both kinetic energy and momentum are conserved. This means that the objects involved do not stick together after the collision and there is no loss of energy.

What is an inelastic collision?

An inelastic collision is a collision in which kinetic energy is not conserved but momentum is still conserved. This means that the objects involved stick together after the collision and some energy is lost in the form of heat or sound.

How does the mass and velocity of objects affect the momentum in a collision?

The momentum of an object is directly proportional to its mass and velocity. This means that objects with greater mass or velocity will have a greater momentum in a collision.

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