1.) A 10,000 kg railroad car traveling at a speed of 24.0 m/s strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed afterward?

2.) A 3.0 kg ball at 3 m/s and strikes a 1.5 kg ball moving at -2 m/s. After the collision, the 1.5 kg ball moves to the right at 2 m/s. What is the final velocity of 3.0 kg ball?

3.) A 85 kg running back is moving at +12 m/s and strikes a 125 kg linebacker moving at -8.0 m/s. What is the final velocity if they stick together?

Formula: m1vi+m2vi=m1vf+m2vf

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1. the final momentum is (M1+M2)V

2. just do the math.
3. same as 1, if they stick together, final momentum (85+125)V solve for v.

Sure, I can help you with these problems. To solve them, we will use the principle of conservation of momentum. This principle states that the total momentum before a collision is equal to the total momentum after the collision, as long as no external forces are acting on the system.

Let's solve each problem step by step:

1.) A 10,000 kg railroad car traveling at a speed of 24.0 m/s strikes an identical car at rest. If the cars lock together as a result of the collision, what is their common speed afterward?

To find the common speed of the cars after the collision, we need to apply the conservation of momentum principle. The total momentum before the collision is the sum of the individual momenta of the two cars. Since one car is at rest, its initial momentum is zero.

So, the equation becomes:

(10,000 kg * 24.0 m/s) + (0 kg * 0 m/s) = (10,000 kg + 0 kg) * final velocity

Simplifying, we have:

240,000 kg * m/s = 10,000 kg * final velocity

Dividing both sides of the equation by 10,000 kg, we get:

24.0 m/s = final velocity

Therefore, the common speed of the cars after the collision is 24.0 m/s.

2.) A 3.0 kg ball at 3 m/s strikes a 1.5 kg ball moving at -2 m/s. After the collision, the 1.5 kg ball moves to the right at 2 m/s. What is the final velocity of the 3.0 kg ball?

Again, we will apply the conservation of momentum principle. The total momentum before the collision is:

(3.0 kg * 3 m/s) + (1.5 kg * -2 m/s)

So, the equation becomes:

(3.0 kg * 3 m/s) + (1.5 kg * -2 m/s) = (3.0 kg + 1.5 kg) * final velocity

Simplifying, we have:

9 kg * m/s - 3 kg * m/s = 4.5 kg * final velocity

Dividing both sides of the equation by 4.5 kg, we get:

2 m/s = final velocity

Therefore, the final velocity of the 3.0 kg ball is 2 m/s.

3.) A 85 kg running back is moving at +12 m/s and strikes a 125 kg linebacker moving at -8.0 m/s. What is the final velocity if they stick together?

Once again, we will use the conservation of momentum principle. The total momentum before the collision is:

(85 kg * 12 m/s) + (125 kg * -8.0 m/s)

So, the equation becomes:

(85 kg * 12 m/s) + (125 kg * -8.0 m/s) = (85 kg + 125 kg) * final velocity

Simplifying, we have:

1020 kg * m/s - 1000 kg * m/s = 210 kg * final velocity

Dividing both sides of the equation by 210 kg, we get:

2 m/s = final velocity

Therefore, the final velocity of the combined mass is 2 m/s.

I hope this helps! Let me know if you have any further questions.