1. If a rocket is shot vertically upward from the ground with an initial speed of zero, under a thrust force Fo that is constant and lasts for a period of to, what will be the maximum height reached by this rocket and when will that happen? You should use a particle model for the rocket, with mass m, and assume a constant gravitational acceleration g. Air resistance can be ignored during the boost period of Osts to. After the boost period, i.e. t 2 to, air resistance is not negligible and can be represented by a second order model, cv?, in which v is the vertical speed of this rocket. You should set t = 0 and y = vertical displacement = 0 at the moment when the thrusts starts. 2. (a) Using the analytical result from problem #1 above, let mass = 0.5 kg, quadratic air resistance constant c = 0.01 N-S3/m², g = 9.8 m/s?, Fo = 70 N and to = 0.2 s, find the maximum height reached by this rocket and the time instant when that happens. (b) Using Excel, develop a simulation program for the rocket flight described in part (a) and find the maximum height reached by this particle. Does the numerical and analytical results agree with one another? (c) Modify your Excel software so that it predicts the maximum height reached by this rocket when air resistance is also included during the boost phase i.e. Oststo. 3. Develop an Excel program and use it to (a) repeat problem #2 of Homework #1 and compare the results; (b) repeat problem #3 of homework #1; (c) repeat problem #3 of homework #1 with weight of the rocket reduced to 1 lb.