thought experiment that shows hor the 3rd principle fails on spirals

im in a 10 m tower, a 1kg cannonball is shot underneath me horizontally at 10 m from me and im holding a cable that is tight to the ball, for the ball to make a circle the tension shown in a dinamometer put in the cable would be v*v*m/r= 1000N being the speed of the ball 100 m/s

i shoot the ball again and this time i let the cable slip or glide away in my hands in such a way that the tension shown is 100 N, lets neglect transformation of friction into heat, gravity and cable weight

how long will it take the ball to reach my horizontal?


what radius will have the cable when the ball is at my horizontal?

when the ball is at my horizontal going to my vertical what constant tension would show the dinamometer if when the ball reached my vertical had to have 10 m radius again by my having pulled the cable?

how long will it take it to reach my vertical?

the cable is pulled or let away by crancking the cable(rigid in this case) and the spinning axe in such a way that for every grade the axe spins the cable retracts or spands one meter or whatever necesary