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**1. This was a hard test question that I took partial credit on. I want to fully understand what I did wrong so that I’m fluid with the concept. I’m also new to this forum. I love constructive criticism too! lol**

Zombie Apocalypse has arrived and the war has begun. Your task as a physics student is to gather intel on the Kinetic energy lost due to the collision of darts on their vulnerable heads. Your crossbow can be modeled as a spring with a 1500N/m constant that can be drawn back to a 32cm maximum. You shoot your 35.0 gram crossbow dart at the zombie's 5.1kg head, striking it horizontally level as fired from your position. The dart buries itself in the zombie's head, and the head slides back across the level table. The CIA needs the fractional amount of Kinetic energy lost in the collision compared to the initial kinetic energy, that is, [delta KE]/KEi

Zombie Apocalypse has arrived and the war has begun. Your task as a physics student is to gather intel on the Kinetic energy lost due to the collision of darts on their vulnerable heads. Your crossbow can be modeled as a spring with a 1500N/m constant that can be drawn back to a 32cm maximum. You shoot your 35.0 gram crossbow dart at the zombie's 5.1kg head, striking it horizontally level as fired from your position. The dart buries itself in the zombie's head, and the head slides back across the level table. The CIA needs the fractional amount of Kinetic energy lost in the collision compared to the initial kinetic energy, that is, [delta KE]/KEi

**2. Homework Equations :**

Crossbow Dart KE= 1/2kx^2

Conservation of Momentum

Before Collision- Pi= m1v1 + m2v2= kg/m/s

KEi= 1/2m1v1^2 + 1/2m2v2^2= Joules

After Collision- P’= m1v1’ + m2v2’= kg/m/s

KEf= 1/2m1v1^2’ + 1/2m2v2^2’= Joules

…m1v1=(m1+m2)v2

Crossbow Dart KE= 1/2kx^2

Conservation of Momentum

Before Collision- Pi= m1v1 + m2v2= kg/m/s

KEi= 1/2m1v1^2 + 1/2m2v2^2= Joules

After Collision- P’= m1v1’ + m2v2’= kg/m/s

KEf= 1/2m1v1^2’ + 1/2m2v2^2’= Joules

…m1v1=(m1+m2)v2

**3. I tried a few different things, more or less throwing mud on the wall to see what sticks at minimum. But here goes…**

1. Crossbow Dart KE= ½(1500N/m)(0.32m)^2= 76.8J

2. Solve for V1, ½(0.035kg)(v)^2=(1500N/m)(0.32)^2

….Result 66.25 m/s

3. Solve for V2, (0.035kg)(66.25m/s)= (0.035kg + 5.1kg)v2

….Result 0.451557 m/s …0.45 m/s

4. This is where I think I’m lost…delta KE/KE? Up to this point I hope this is right?

1. Crossbow Dart KE= ½(1500N/m)(0.32m)^2= 76.8J

2. Solve for V1, ½(0.035kg)(v)^2=(1500N/m)(0.32)^2

….Result 66.25 m/s

3. Solve for V2, (0.035kg)(66.25m/s)= (0.035kg + 5.1kg)v2

….Result 0.451557 m/s …0.45 m/s

4. This is where I think I’m lost…delta KE/KE? Up to this point I hope this is right?

Thank you all for the guidance