Solving Force and Motion Problems with the SUVAT Equations

[Originaltitle]

Homework Statement

Homework Equations

F=ma to find the respective accelerations of the man and the barrel.
The suvat equations.

The Attempt at a Solution

I tried making 2 equations to solve them simultaneously but the values I'm looking to find always cancel out.
I know that s and t will be the same for the barrel and the man when the bottom of the barrel is level with the man's head. But how do I find either s or t?

 

[ehild]

Use conservation of energy.

ehild

 

[Originaltitle]

Could you be more elaborate, please? I mean, if I were to use conservation of energy, I'd need to use W.D.=Fx, K.E.=1/2mv^2 and G.P.E.=mgh. For W.D., I may find F but I don't know x. For K.E., I know m but not v. For G.P.E. I don't know h. How am I to find h?

 

[ehild]

The man raises as much as the barrel sinks and they meat halfway, that is at 9 m height.
Both man and barrel are in rest initially. The barrel has some potential energy with respect to the ground.
when they meet at 9 m height, both have potential and kinetic energy, and both move with the same speed v, you have to find.

ehild

 

[Originaltitle]

That is if we assume that they meet halfway - nowhere in the question does it say they meet halfway. If they do meet halfway, the g.p.e. of the man = 800*100*9=720000J and the barrel's loss in g.p.e. = 1200*100*9=1080000J. If we say the loss in g.p.e. = gain in k.e., then 1080000 = 0.5*80*v^2. V^2 = 27000. V = 164? That's not an option. Where'd I go wrong?

 

[MrWarlock616]

Well, for starters, you don't have to convert the masses into grams as the SI unit is kg.

Also, you need to find the velocity of the man when the bottom of the barrel lines up with the man's head. Logically, this would happen halfway.

By conservation of energy, the total energy at the start equals the total energy in the halfway position. So, just consider the system of man and barrel and use $P.E._1+K.E._1=P.E._2+K.E._2$

 

[ehild]

That is if we assume that they meet halfway - nowhere in the question does it say they meet halfway.

The length of the chord does not change. As much the left piece gets shorter that much the right piece becomes longer. When man and barrel are at the same level, they are at equal distances from the initial positions of man and barrel.

ehild