I have no idea how i keep getting the wrong answer. Here's what i did
At the top of the trajectory the horizontal velocity is the same which is
cos(35)(125).

By using conservation of momentum i can find the velocity of fragment 2

MVix = MVfx
(28)(cos(35)(125)) = (14)(0) + (14)(Vf2x)
So i just find Vf2 which is 204.788011 m/s

Well to calculate range i need to know the max height, but we also need the time it reaches max height. So to find time that reaches max height:

Everything you have done, except one part, is correct and quite clear.

You had,

(Horizontal velocity of fragment 2) / (time it takes for the object to fall 262m) = the range of fragment 2

That should be a multiply sign, not a division sign, giving

(Horizontal velocity of fragment 2) x (time it takes for the object to fall 262m) = the range of fragment 2

There's just a semantic problem, perhaps.
The Fragment2 doesn't actually exist until until the explosion a the top of the flight. So, its range may simply be the horizontal distance travelled in the time it takes to fall to the ground.

Just calulating the range of Fragment 2, i still got the wrong answer. (by the way it's an electronic questionaire that tells you if you get the answer right or wrong if you submit the answer).

And i checked all the numbers many many times.

I don't know if this is allowed but could somebody do the question and can we compare answers?

My answer was roughly 42m
and the Range of the Fragement is roughly 28m

I made a mistake in my first post. I'm afraid I mis-read your text. I really should wear my specs.

You had,

(Horizontal velocity of fragment 2) / (time it takes for the object to fall 262m) = the range of fragment 2

That should be a multiply sign, not a division sign, giving

(Horizontal velocity of fragment 2) x (time it takes for the object to fall 262m) = the range of fragment 2

The time to fall the 262 m is the same as the time to get up there. i,e t = 7.3085 s.
Horizontal velocity is Vx = 204.788011 m/s
Range = (Horizontal velocity) x (The time to fall the 262 m) = 204.788011 m/s x 7.3085 s. = 1496.693 m

OH my goodness!!! Thank you so much!!!
and by the way the wording of the question is SOOO bad, because when i enter 1496.693 it says i'm wrong, because the question is refering to the range from the initial firing position. While the question is misleading to us thinking that it's just the range of Fragment 2, but i got the right answer. Thanks a lot