Halliday, Resnick & Walker — Potential Energy and Conservation of Energy: Problem 132

Redesigning a track. Figure 8.55 shows a small block that is released on a slope, which then slides through a valley and up onto a plateau and then through a distance \(d = 2.50\text{ m}\) in a certain time \(\Delta t_1\). The whole track is frictionless, and the height difference \(\Delta h = h_1 - h_2\) between the release point and the plateau is \(2.00\text{ m}\). You want to decrease the time through \(d\) by \(0.100\text{ s}\). What should the value of \(\Delta h\) then be?