Solution: (1) According to Newton's second law and centripetal force formula,

F-mg=mrω2，

So ω =? √F-mg/mr？ = 8 radians/second,

That is, the rope is broken and the angular velocity of the ball is 8 rad/s.

(2) From V=rω, it can be concluded that the linear speed of the rope breaking into balls is V=8m/s,

After the rope broke, the ball made a flat throw motion.

Horizontal direction: x=V0t?

Vertical direction: h= 1/2 gt2.

Substitute into numerical solution? x=8m

The horizontal distance between the falling point and the throwing point is 8m.

Analysis: (1) The rope is broken, and the tension of the rope is exactly 74N. According to Newton's second law and centripetal force formula, angular velocity can be obtained.

(2) After the rope is broken, the ball moves horizontally, and the horizontal distance between the landing point and the throwing point can be obtained according to the law of horizontal throwing movement.