Okay we have this problem: 50 kg mass traveling at 10 m/s strikes a 100kg mass at rest find the final velocity each....if...

1. it is elastic

2. if it isnt elastic

i know for an elastic something has to be 100% like 100% of momentum is conserved. I don't know how to set up equations for this logically i know 1/2mv^2 is Ke and mv=p

Whoever created this problem does not understand inelastic collisions. There are an infinite number of possibilities to (2) if the two masses do not stick together. The sticking-together case is probably what they meant.

There are also many possibilities for an elastic collision (1), unless both masses continue along the same direction. Depending upon where one billiard ball hits another, they can go in many directions, but all are elastic collisions.

I am not surprised you are confused by this question. You deserve a better teacher.

For the inelastic "stick-together" case, both masses leave with the same velocity, V2.

50 kg*10 m/s = 150 kg*V2
Solve for V2
V2 = 3.33 m/s, along the same direction as the initial velocity.

The elastic case is harder. You have to solve simultaneous equations of momentum and kinetic energy conservation, with two unknowns. I'll leave that one up to you.

To solve this problem, we can use the principles of conservation of momentum and kinetic energy.

Let's start with the case where the collision is elastic:

1. Elastic collision:
In an elastic collision, both momentum and kinetic energy are conserved. We will use these conservation laws to find the final velocities.

First, let's find the initial momentum and kinetic energy before the collision:

Initial momentum: The momentum before the collision can be calculated as the product of mass and velocity for each object.
Initial momentum of the 50 kg mass: p1 = mass1 * velocity1 = 50 kg * 10 m/s = 500 kg·m/s
Initial momentum of the 100 kg mass (at rest): p2 = mass2 * velocity2 = 100 kg * 0 m/s = 0 kg·m/s

Initial kinetic energy: The kinetic energy before the collision can be calculated using the formula 1/2 * mass * velocity^2.
Initial kinetic energy of the 50 kg mass: KE1 = 1/2 * mass1 * velocity1^2 = 1/2 * 50 kg * (10 m/s)^2 = 2500 J
Initial kinetic energy of the 100 kg mass (at rest): KE2 = 1/2 * 100 kg * (0 m/s)^2 = 0 J

Since the collision is elastic, both momentum and kinetic energy are conserved:

Conservation of momentum:
p1 + p2 = p3 + p4

After the collision, the 50 kg mass and the 100 kg mass will have final velocities, let's call them v3 and v4 respectively.

Conservation of kinetic energy:
KE1 + KE2 = KE3 + KE4

Now, let's substitute the initial values and solve for the final velocities.

p1 + p2 = p3 + p4
500 kg·m/s + 0 kg·m/s = 50 kg * v3 + 100 kg * v4

KE1 + KE2 = KE3 + KE4
2500 J + 0 J = 1/2 * 50 kg * (v3)^2 + 1/2 * 100 kg * (v4)^2

You have two equations with two unknowns (v3 and v4). Rearrange and solve these equations simultaneously to find the final velocities.

Now let's move on to the case of an inelastic collision:

2. Inelastic collision:
In an inelastic collision, momentum is conserved, but kinetic energy is not conserved.

Using the conservation of momentum, as mentioned earlier, we have:

p1 + p2 = p3 + p4
500 kg·m/s + 0 kg·m/s = (50 kg + 100 kg) * v

Since the masses stick together after collision, their sum becomes the final mass:

150 kg * v = 500 kg·m/s

Solve for v to find the final velocity in case of an inelastic collision.

That's how you can approach both elastic and inelastic collisions and find the final velocities using the principles of conservation of momentum and kinetic energy.