What is the Optimal Angle for a One-Bounce Baseball Throw?

[TN17]

1. In baseball, player throws ball so that the ball takes one bounce before it reaches infielder.

Suppose that the angle at which a bounced ball leaves the ground is the same as the angle at which the outfielder launced it.

The ball's speed after the bounce is half of what it was before the bounce.

a) Asumming the ball is always thrown with same initial speed, at what angle should the ball be thrown in order to go the same distance "x" with one bounce as a ball thrown upward at 45 degrees with no bounce?

b) Determine ratio of the times for the one-bounce and no-bounce throws.

The Attempt at a Solution

I've attempted this question all afternoon, but with all the equations I have, there is more than one unknown.
I'm very confused and it would be greatly appreciated if you helped me.
Thank you. :)

 

[Moneries]

equate range of the 45 degree throw and the sum of the ranges of the first throw and the bounce
assume y = angle of throw
Vo^2sin90/g = Vo^2sin2y/g + Vo^2sin2y/2g ------ equating ranges
Vo^2/g = Vo^2sin2y(1.5)/g ------ factor out variables
3/2 = sin2y------ dividing both sides by (Vo^2/g)
y= 27 and 63degrees.