Catapult Projectile Range: Calculate w/Varied Mass

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a catapult that shoots at 45 degrees, with counterweight on one side.
the catapult is similar to a see-saw, where projectile is placed on one end, and the counterweight to another end.
the counterweight is lifted to a 45degrees and released.

is there any way to find the theoretical range of the projectile... when changing the projectile mass.
 
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If one ignores air resistance and assumes that the launch velocity is invariant, then the range of the projectile will be independent of it's mass.
 
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thanks for the prompt reply.
i was wondering whether there are any equations to find the theoretical range of the projectile been thrown off the catapault. as I am comparing my results to the theoretical results.