Maximum Projectile Speed for Safe Hanging: 20kg Wood Ball and 2m Long Wire

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To determine the maximum speed of a 1.0 kg projectile that can hit a 20 kg wood ball hanging from a 2.0 m wire without breaking it, conservation of momentum and centripetal force equations are essential. The maximum tension the wire can handle is 400N, which limits the speed of the projectile. After applying the relevant physics principles, the calculations reveal the largest permissible speed. The original poster expressed frustration but ultimately found the solution with assistance. This highlights the importance of understanding momentum and tension in solving physics problems involving hanging objects.
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Look I really need someone's help, I spent over 3 hours on this problem and can't figure it out. If anyone could tell me what to do (try being specific), I'd appreciate.

A 20kg wood ball hangs from a 2.0m longwire. The maximum tension the wire can withstand without breaking is 400N. A 1.0 kg projectile traveling horizontally hits and embeds itself in the wood ball. What is the largest speed this projectile can have without causing the cable to break?

Please anyone, I really need to get this.
 
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Use conservation of momentum to determine what speed the ball will have when it is struck by the projectile. Use the equation for centripetal force to determine the tension in the wire. You should be able to go from there.
 
Actually, I really can't figure it out, I read what you said, but nothing adds up.
 
I got it, OMG I got it, thank you sooooo much. God why didn't i think of that. Thx very much.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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