Final answer:
In physics, for projectile motion without air resistance, the optimal launch angle for maximum range is 45 degrees, and the angle of maximum perpendicular weight component on an inclined plane as well as the angle between tangential velocity and centripetal force vectors is 90 degrees.
Step-by-step explanation:
The question pertains to the domain of physics, specifically to the kinematics of projectile motion. When a projectile is launched on level ground, the angle that maximizes the range of the projectile is 45 degrees. This is under the assumption that air resistance can be neglected. For an angle of incline on an inclined plane, the perpendicular component of weight is at its maximum at 90 degrees. The angle between the vectors of tangential velocity and centripetal force is 90 degrees since they are perpendicular to each other. Lastly, when discussing the torque on a current loop, it varies based on the sine of the angle between the magnetic field and the normal to the loop's area.