Two teammates are playing catch, indoors, with a baseball, where the ceiling height is 4.53mm. The first teammate releases the ball at a height of 1.97mm with a velocity of 25.2m/sm/s, and the second teammate catches it at the same height. Neglect the diameter of the baseball.

a. What is the maximum vertical component of the velocity, in meters per second, such that the baseball does not hit the ceiling?

b. At what angle above the horizontal, in degrees, is the baseball thrown if it passes just below the ceiling.

c. What is the horizontal distance, in meters, between the two teammates?

d. To achieve the maximum range, the baseball would be thrown at an angle of 4545. If the two teammates moved outside, where the ceiling does not pose a height constraint, what is the maximum horizontal distance, in meters, at which the they could play catch using the numbers provided in the problem statement?