Final answer:
To address the questions about projectile motion and angular velocity, the range of a projectile is zero at angles of 0° or 90°, the optimum angle for maximum distance is 45°, the angle between tangential velocity and centripetal force is 90°, one radian equals approximately 57.3°, and the maximum perpendicular weight component on an incline occurs at a 90° angle.
Step-by-step explanation:
Projectile motion and angular velocity are fundamental concepts in physics that describe the movement and orientation of objects in space. To answer the specific questions available:
- For a projectile, the range would be equal to zero when the angle of launch is c. 90° or 0°, because at these angles the projectile either goes straight up and comes down (90°) or is not launched at all (0°), resulting in no horizontal displacement.
- The optimum angle for a projectile to achieve the maximum distance is b. 45°. This angle balances the vertical and horizontal components of the projectile's velocity equally, assuming no air resistance.
- The angle between the vectors of tangential velocity and centripetal force is always c. 90° as they are perpendicular to each other.
- One radian is approximately a. 57.3° when converted to degrees.
- Given a radius of a clock and the arc length, you can find the angle of rotation between the two hands using the formula θ = s/r, where θ is the angle in radians, s is the arc length, and r is the radius. Converting radians to degrees after calculation would give the answer in degrees.
- On an inclined plane, the perpendicular component of the box's weight is at its maximum when the angle of incline is d. 90°, which is straight up.
Overall, a solid understanding of angles in projectile motion and rotation can help in solving various physics problems accurately.