Projectile help - really confused

[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.


3. 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. :)

 

[zgozvrm]

In general, this question is a good one, but as stated, doesn't make much sense.

Neglecting air resistance (or other outside influence other than gravity), a projectile will hit the ground at the same angle it was launched only if it was launched at the same elevation as it lands (except for the case when the projectile is launched vertically which, in this problem, that won't get the ball to another player).

It is highly unlikely that this would be the case (that the ball would be launched from the same elevation as it hits the field), since baseball fields are generally flat and players don't throw balls from ground level, but from a standing position. So, the ball (projectile) is launched at an altitude of approximately 6 feet above the field. This means that the launch angle will actually be less than the angle of impact.

 

[zgozvrm]

Given what I think is meant by this question, it appears that part (a) is looking for the launch angle that will result in half the distance of a ball thrown at 45 degrees for any given speed (assuming that the ball is launched from ground level).

There are 2 answers: one greater than 45 degrees and one less than 45 degrees. It's unlikely that a baseball player would want to throw a ball at an angle greater than 45 degrees, as that would require more time for the ball to get to it's target.