Lab 02 Expectations

Submit plots: pplane – 3, 4, 5a, 5b, 6; fplot – 6.

Units in this lab is important. Make sure you express your answers in the correct units.

1. Nothing is required. Note: this will work if you substitute t for y in dfield.
2. Make the graph (using pplane7), but you won’t plot it until a later question.
3. Pplane plot, with 4 solutions. For the solutions that have a maximum height, what is it, in miles? For the solutions that go off the screen, approximate the limiting value as t goes to infinity in miles/sec. Turn in un-zoomed plot.
4. Plot orbit that goes through (10, 0). What is the initial velocity (to 2 decimals) of this orbit corresponding with x = 0? Then convert that initial velocity to miles/sec.
5. Solve equation (D) with initial condition v = v0. Show your work! You should get the equation shown.
1. For v0 = 1, what is the maximum value for y? Do this both graphically and using the formula.
2. For v0 = sqrt(2), find the terminal velocity, that is find v, as y -> infinity (use limits and show this in the graph).
3. Find the escape velocity using this formula.
6. Now we add air resistance. Repeat number 2 using equation (E). What is the new estimated escape velocity in miles/sec? Solve equation (E) analytically. Don’t worry about why the object escapes. Plot the E(v) function using fplot.
7. Find the escape velocity with k = . 1/seed. This will require you to resolve the equation from number 6 using this new k value.