Hitting a billiard ball h above centerline

[CrazyDolphin]

Homework Statement

A billiard ball, initially at rest, is given a sharp impulse by a cue. the cue is held horizontally a distance h above the center line. the ball leaves the cue with a speed vo, and because of its "forward English", eventually acquires a final speed of 9vo/7. Show that h=4R/5, where R is the radius of the ball.

Homework Equations

The Attempt at a Solution

I've tried using FRsin(θ)=Iα and coming up with h = (2/5)R^2(α/a). Then using the impulse equation a = v0/Δt and α= ω0/t i got h=(2/5)R^2(ω0/v0). The thing is I keep getting wrong and contradictory answers about ω0.

 

[Spinnor]

See problem # 4,

http://ocw.mit.edu/courses/physics/...lation-dynamics/MIT8_01SC_problems27_soln.pdf

Found via Google search,

"Hitting a billiard ball h above centerline impulse rotation answers"