an astronaut on the moon fires a projectile from a launcher on a level surface so as to get the maximum range. If the launcher gives the projectile a muzzle velocity of 25 m/s what is the range of the projectile?

Answer 1

I am going to assume that you know that maximum range happens when cos theta = sin theta = .707 or at 45 degrees from horizontal. I can show you if you need that derivation.
So using 45 degrees for angle of launcher and gravity = g on earth /6 = 9.8/6 = 1.63 m/s^2
horizontal speed = 25 cos theta = 25^.707 = 17.7 m/s the whole time
Initial vertical speed, Vo = 25 sin theta = 17.7 as well
v = Vo - 1.63 t
halfway through the trip, the vertical velocity is zero and it starts down
so
0 = 17.7 - 1.63 (t/2)
so t = 21.7 seconds in air (if any)
how far does it go in 21.7 seconds?
d = 17.7 (21.7) = 384 meters

Answer 2

How did you get the angle?