Abox on a slope slides under the following force f = m*g*sin(theta) - 0.2v(t). assume m = 1kg and g=10 and theta = 30'. we want to simulate the slide using dt = 0.1 second interval. this means update frame rate is 10 per second. initial speed is 0. after 2 seconds we like to know what is the current position and speed of the box. we want to do this using explicit euler(ee), semi-explicit euler(se), and verlet method for updating at each frame.
a) what are the update equations for ee method?
b) what are the update equations for se method?
c) what is the update equation for verlet method? how do you choose the initial first 2 positions in this method?
d) provide a table showing updates per frame for each method. this means there are 3 columns, one for each method, and there are 20 rows for 20 frames to comprise 2 seconds of updates. which method is more out of sync with the other 2 methods?
e) what is the maximum speed of decent of the box on the slope? why? (hint. use analytical way to argue what is the maximum speed)