I found some good web pages with highly detailed answers to predicting the range of a trebuchet. A very simple model we have used in my Intro to Eng class just uses the mass of the projectile (m2), the mass of the counter weight (m1), and the height the counter weight falls (h):
Range (max) = 2 * (m1/m2) * h
Now the efficiency of the trebuchet will cause this model to be off by quite a bit. But once you have a working trebuchet, we find this model works well when we vary m1, m2, or h. We assume we have a take off angle of 45 degrees above the horizon.
This solution is based on the classic max range ballistics problem - 45 degree take off angle. It also assumes converting all the potential energy of the counter weight to kinetic energy of the projectile. That is why the efficiency issue comes up as a lot of energy is lost due to friction in the moving trebuchet. If the projectile spins a lot then it will travel a shorter distance as the potential energy is split into kinetic and rotational energy. Projectile shape and wind will also vary the results.
Good luck.
Density means how much mass is concentrated in the given 3d space .thus the more the density the more mass is occupied in the less space.. and thus the objects with lesser density floats on the object with higher density
Explanation:
You have already determined the components of the known forces so I won't repeat your work here. Since the resultant force 
and F1 are completely along the x-axis, we can conclude that
We can now solve for the magnitude of 
The angle 
is then
or
Answer= D. Velocity includes a direction; speed does not.
Velocity and speed both have the same units of m/s, so answers A and B are wrong.
Velocity is a vector quantity and so has direction and magnitude, so C is wrong.
Speed is a scalar quantity, only having magnitude and no direction.
