Final answer:
The sum of the angles in a triangle is 180 degrees, which is the correct expression rather than 360, 90, or 270 degrees. For a projectile, a range of zero occurs at a launch angle of 90° or 0°. The angle between tangential velocity and centripetal force is 90°, and the optimum projectile launch angle for maximum distance is 45°.
Step-by-step explanation:
The sum of the angles of a triangle can be expressed in two ways, either as 180 degrees or through the sum of its individual angles. The correct answer to this question is a. 180 degrees. Every triangle, regardless of its type, has internal angles that add up to 180 degrees. This is a fundamental concept in geometry known as the Triangle Sum Theorem.
For question 69, regarding the angle of a projectile for which its range is equal to zero, the correct answer is c. 90° or 0°. If a projectile is launched straight up or straight down (at 90° or 0° to the horizontal), it will not cover any horizontal distance, thus having a range of zero.
For question 45, the angle formed between the vectors of tangential velocity and centripetal force is c. 90°. This is because tangential velocity is always directed along the tangent to the path of motion, while centripetal force is directed towards the center of the circle, making them perpendicular to each other.
The optimum angle for a projectile to cover the maximum horizontal distance, mentioned in question 86, is b. 45°. This is due to the fact that at 45°, the horizontal and vertical components of the projectile's velocity are equal, maximizing the range according to projectile motion equations.