Question

Reexamine the Brachistochrone problem done in class and show that the time required for a particle move (frictionless) to the miniμm point of the cycloid is ____, independent of the starting point. Remember that a is a constant.

a) π × the square root of a
b) Half the square root of a
c) Twice the square root of a
d) Square root of a

Answer 1

The time required for a particle to move to the minimum point of a cycloid in the Brachistochrone problem is independent of the starting point and is equal to π times the square root of a.

Step-by-step explanation:

The Brachistochrone problem involves finding the curve along which a particle will move from one point to another in the shortest amount of time under the influence of gravity. In this problem, it is shown that the time required for a particle to move to the minimum point of a cycloid is independent of the starting point and is equal to π times the square root of a.