Final answer:
The angle formed between the vectors of tangential velocity and centripetal force is 90°.
Step-by-step explanation:
The angle that the vectors of tangential velocity and centripetal force form is 90°. The tangential velocity vector is perpendicular to the centripetal force vector, resulting in a right angle between them.
When considering the components of a vector, the x-component will be greater than the y-component when the angle (θ) of the vector is between 0° and 45°. Specifically, 0° < θ < 45°. This is because as the angle increases from 0° to 45°, the x-component (which is based on the cosine function) starts at its maximum and decreases, while the y-component (based on the sine function) starts at zero and increases. When the two are equal at 45°, any increase in angle beyond this will result in the y-component becoming larger than the x-component. For the angle of a projectile where its range equals zero, the answer is when the angle is at 90° or 0°. At 90°, the projectile is going straight up and coming straight down, and at 0°, it has no vertical component to create a range. Lastly, the optimum angle for a projectile to achieve maximum distance is 45° as it provides the best balance between vertical and horizontal components of motion.