Final answer:
The angle formed between the vectors of tangential velocity and centripetal force is 90 degrees because they are perpendicular. For a projectile, the range is zero when the angle of projection is either 0 degrees or 90 degrees.
Step-by-step explanation:
Understanding Angles in a Circle
In the context of circular motion and geometry, there are certain angle relationships between tangents, radii, and the forces or velocities involved. A tangent to a circle is a line that touches the circle at exactly one point and is perpendicular to the radius at the point of contact. The angle formed by a tangent line and the radius at the point of contact is always 90 degrees (right angle).
Regarding the question about vectors in circular motion: the vector of tangential velocity is always perpendicular to the vector of centripetal force because the tangential velocity is directed along the tangent to the circle's path, while the centripetal force is directed towards the center of the circle, along the radius. This establishes a right angle between them. Thus, the angle formed between the vectors of tangential velocity and centripetal force is 90 degrees.
Moving on to the question of a projectile's angle for zero range, recall that the maximum range of a projectile occurs at an angle of 45 degrees. However, when the angle of projection is 0 degrees or 90 degrees, the range becomes zero as the projectile either moves horizontally without any vertical motion or moves vertically without horizontal motion, respectively.