_ Introduction: In the rst Computational assignment, you investigated the motion of a free-falling object, meaning that you neglected the effect of air resistance. Solving a problem that includes air resistance is mathematically more complicated, because the model for air resistance depends on velocity (the time derivative of displacement). It is possible to nd an analytical solution, but it requires knowledge of differential equations. Finding a solution (trajectory) using computational tools, instead, requires a minimal effort in addition to the free-falling object problem. We are going to investigate the motion of an object falling vertically (1 dimensional), extending the problem to projectile motion (2 dimensional) requires a small extra effort. Before we look at the computational methods, we need to understand the effects of air resistance. Refer to the textbook for a deeper explanation of air resistance, for this assignment we simply assume that it acts against the direction of motion and it depends on the square of velocity as: FAR = _C 1721'). 1. Start with an object that is going up (no horizontal motion), right after it receives the initial push (it is no longer in contact with anything). Draw a complete free body diagram. What do you expect it happens to the upward momentum? Why? 2. After a short time, the velocity is less (say, half the initial). What happens to the magnitude of the force due to air resistance? How does it affect momentum, with respect to part 1? 3. What is the velocity at the highest point of the trajectory? What is the force due to air resistance? Draw a ee body diagram at this stage. 4. Draw the free body diagram of the object when it has started to fall down. 5. How large do you think is the air resistance force, with respect to the weight force, when the object just began to go down? Why? 6. What do you expect it happens to the magnitude of velocity? If velocity increases, what happens to the force due to air resistance? When the object is falling, the air resistance force keeps increasing and eventually it reaches the same magnitude as the weight force. What is the net force, at that moment? How does momentum change? From that moment on, air resistance stays constant, the net force stays constant, and both momentum and velocity no longer change; this is terminal velocity. The activity. The best option, for this activity, is to modify the code you used for the first assignment (HWC01). Make sure you save a copy of the old code, before you start modifying the new one. Use the same initial conditions (position, velocity, and mass) as the free-falling object problem. Then you can change the code like the following. 9. Add the constant C = 1 to the initial conditions (air resistance coefficient). 10. It is useful, before entering the loop, to define the velocity of the object (it will make it easier to include it in the first iteration of the loop). v_cart = v0 # set velocity 1 1. Set the sum of forces in the first line of the loop). You can find useful to set the velocity magnitude and unit vectors with v_cart.mag v_cart.hat 12. Run the code. Save the plots of position, velocity, and acceleration. Discuss how the plots compare with the discussion in the introduction (parts 1 to 9), how do velocity and acceleration evolve? 13. Repeat the investigation by changing the constant C, then by changing the initial position, finally by changing the initial velocity. Save the plots, making sure they are properly labeled to identify what you changed. Discuss how the new initial parameters affect the motion (refer to the plots). 14. Create a file with a link to your code on Glowscript, your answers, the results, and the plots. 15. For extra credits, follow the Glowscript manual to include arrows that follow the direction of the weight force, air resistance force, and net force