Problem 1: Use python in jupyter notebook, provide your code and resulting plots. In class we derived the two parametric equations that determine the path (x, y) of a brachistochrome, with the roller coaster starting from rest at (0,0). Note the y-axis is chosen to point down. x= a[e-sin(0)] and y = a (1 -cos(0). Let's design a brachistochrome, such that its path intersects point B at (3.0 m, 4.0 m). Neglect friction. 1- Use python to determine the value of the integration constant a to two significant figures. You need to explain and show to me your method of approach and code/plots to find a. 2- Make a plot showing the path from the origin, through point B and to its lowest possible point, also on the plot mark point B clearly. 3- What is the speed of the roller coaster at point B? 4- What is the speed of the roller coaster at the lowest point along the path? Problem 1: Use python in jupyter notebook, provide your code and resulting plots. In class we derived the two parametric equations that determine the path (x, y) of a brachistochrome, with the roller coaster starting from rest at (0,0). Note the y-axis is chosen to point down. x= a[e-sin(0)] and y = a (1 -cos(0). Let's design a brachistochrome, such that its path intersects point B at (3.0 m, 4.0 m). Neglect friction. 1- Use python to determine the value of the integration constant a to two significant figures. You need to explain and show to me your method of approach and code/plots to find a. 2- Make a plot showing the path from the origin, through point B and to its lowest possible point, also on the plot mark point B clearly. 3- What is the speed of the roller coaster at point B? 4- What is the speed of the roller coaster at the lowest point along the path