Help I need the solution for these two

[vincikai]

A 2.30-kg ball, moving to the right at a velocity of +1.29 m/s on a frictionless table, collides head-on with a stationary 6.50-kg ball. Find the final velocities of (a) the 2.30-kg ball and of (b) the 6.50-kg ball if the collision is elastic. (c) Find the final velocity of the two balls if the collision is completely inelastic.




Consult Concept Simulation 7.1 in preparation for this problem. Two friends, Al and Jo, have a combined mass of 169 kg. At an ice skating rink they stand close together on skates, at rest and facing each other, with a compressed spring between them. The spring is kept from pushing them apart, because they are holding each other. When they release their arms, Al moves off in one direction at a speed of 1.15 m/s, while Jo moves off in the opposite direction at a speed of 1.20 m/s. Assuming that friction is negligible, find Al's mass.

 

[Hootenanny]

We do not provide solutions here, we will however, guide you through the question if you are willing to put some effort in

 

[PPonte]

A 2.30-kg ball, moving to the right at a velocity of +1.29 m/s on a frictionless table, collides head-on with a stationary 6.50-kg ball. Find the final velocities of (a) the 2.30-kg ball and of (b) the 6.50-kg ball if the collision is elastic. (c) Find the final velocity of the two balls if the collision is completely inelastic.

(a) and (b)
An elastic collision is one where both momentum and kinetic energy are conserved. Then, to solve this use both equations:

$$m_{1}\vec{v_{1i}} + m_{2}\vec{v_{2i}} = m_{1}\vec{v_{1f}} + m_{2}\vec{v_{2f}}$$

$$\frac{1}{2}m_{1}v_{1i}^{2} + \frac{1}{2}m_{2}v_{2i}^{2} = \frac{1}{2}m_{1}v_{1f}^{2} + \frac{1}{2}m_{2}v_{2f}^{2}$$

(c)
A perfectly inelastic collision is one that two objects stick together during a collision. Only momentum is conserved, which becomes:

$$m_{1}\vec{v_{1i}} + m_{2}\vec{v_{2i}} = (m_{1} + m_{2} )\vec{v_{f}}$$

 

[Office_Shredder]

Consult Concept Simulation 7.1 in preparation for this problem. Two friends, Al and Jo, have a combined mass of 169 kg. At an ice skating rink they stand close together on skates, at rest and facing each other, with a compressed spring between them. The spring is kept from pushing them apart, because they are holding each other. When they release their arms, Al moves off in one direction at a speed of 1.15 m/s, while Jo moves off in the opposite direction at a speed of 1.20 m/s. Assuming that friction is negligible, find Al's mass.

Because there's no friction, the center of mass of the two is going to be motionless. This means their momenta are equal and opposite