<Ol> <Li> At the onset, the angle must be zero when the particle speed is zero . Hence, the brachistochrone curve is tangent to the vertical at the origin . </Li> <Li> The speed reaches a maximum value when the trajectory becomes horizontal and the angle θ = 90 ° . </Li> </Ol> <Li> At the onset, the angle must be zero when the particle speed is zero . Hence, the brachistochrone curve is tangent to the vertical at the origin . </Li> <Li> The speed reaches a maximum value when the trajectory becomes horizontal and the angle θ = 90 ° . </Li> <P> Assuming for simplicity that the particle (or the beam) with coordinates (x, y) departs from the point (0, 0) and reaches maximum speed after falling a vertical distance D: </P>

Explain the brachistochrone problem and draw the solution curve