3.9.2 Gravity optimization
Channel: Jorge Munoz
Date: 29/12/2021

This problem is divided in two. Please check 3.9.1 for the first part.

When an object slides frictionlessly down a plane inclined at an angle θ, its acceleration equals g*sinθ. Suppose that a person on a bike is to coast down a ramp, starting from rest, and then coast back up an identical ramp, tracing a “V.” The horizontal distance is fixed to be 2w, and we want to set the depth of the “V” so as to achieve the minimal possible value t_star for the total time.

1. Based only on units, infer the form of the expression for t_star in terms of w, up to a unitless multiplicative constant.

2. Find the angle that minimizes the time.

3. Complete the determination of t_star by finding the unitless constant.

This is problem 3.32 in Ben Crowell's Mechanics (http://www.lightandmatter.com/mechanics/)