Machine Dynamics: Manual Air Pump Calculation (please check my answer)

[JamesBennettBeta]

mentor note: moved from ME forum hence no HW template.

Summary:: I am stuck into this problem for almost a week now. I think I solved it, but it seems something is wrong. Can someone point me, what is wrong here. It'll be so much helpful.

I am stuck into this problem for almost a week now. I think I solved it, but it seems something is wrong. Can someone point me, what is wrong here. It'll be so much helpful.

 

[haruspex]

The image is a bit too fuzzy for me to read. Please type in your working, as required by the forum rules.

 

[Lnewqban]

Should we assume that the mentioned steady velocity of point C is a vector always perpendicular to CO?

 

[haruspex]

Should we assume that the mentioned steady velocity of point C is a vector always perpendicular to CO?

I assumed it meant a steady tangential speed, not linear velocity.
I haven't come across this velocity diagram technique before. As far as I can make out, the solution is obtained by measurements from a scale drawing, not by algebra.

 

[Lnewqban]

Thank you, haruspex.
I hope the OP can soon show us his work more clearly.