Lesson 3
Modeling Real World Problems

1) Please explain or describe when you think numerical modeling might be useful and/or necessary. For what kinds of problems or situations is it useful? Give at least three specific examples of scenarios or problems for which it is useful.

2) To use the Euler Method to numerically find position, velocity, and acceleration as a function of time, we will use the following set of basic general equations:

a_n = F(x_n-1, v_n-1, t_n-1)/m_n-1
v_n = v_n-1 + a_n-1*Dt
x_n = x_n-1 + v_n-1*Dt
t_n = t_n-1 + Dt

Note: We'll be implementing this in Mathcad. In a given equation, Mathcad can't refer back to a number or variable in the same step (n value), so v_n refers back to v_n-1 and a_n-1.

Given all this and what's in your reading handout, write down what you think the Mathcad equations would be for modeling the motion of a 2d projectile where a drag force F_drag = kv is acting. The key thing here is to use the general expression a = F/m to get a specific expression for the acceleration for this particular problem. (To make the typing simpler, use a notation like "x_n-1" for "x_n-1" and "vx_n" for the x component of v_n, etc.)

3) Suppose you jump out of a "perfectly good airplane" and experience 1d freefall with drag on your way down. If the drag force can be modeled as F_drag = D*v² where v is your speed and D is a constant, and your terminal speed is about 3 m/s with the chute open, which of the following is the best value for the coefficient D?

Note: To check your answer, and to see if your web browser will support using Physlets this semester, please give a Physlet page a try. Important: This page will open in a NEW window, so you'll need to come back to THIS window (using the taskbar) to submit your preflight. If the physlet page does NOT load properly, please tell me what happens, including any error messages it displays, in the comments box below. Thanks. Click this link to get to the physlet page.

1. 0.6 kg/m
2. 6 kg/m
3. 60 kg/m
4. 600 kg/m

You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.

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