Question

6. Many IVPs are autonomous, meaning the independent variable doesn't appear explicitly on the right hand side. Such is the case for the differential equation describing the velocity of a falling object: In this autonomous equation, g is the acceleration due to gravity (32 ft/s2). The first term on the right hand side models the air resistance or drag on the object, and k is a constant that depends on the shape and size of the falling object. The choice of the exponent p is a modeling consideration. It is typically chosen in the 1 to 2 range, witlh larger values chosen for higher velocity settings. In the parts that follow, use Euler's method with h-0.1 on the time range (0,5]. When dealing with autonomous equations, MATLAB doesn't mind at all if we define a function as follows: t (t,y) y 2 We can do this for autonomous differential equations and not need to modify our Euler's method to deal with only one variable instead of two. (a) (2 points) A skydiver jumps out of a plane, with k/m 1.6 and p-1, what does the terminal velocity of the skydiver appear to be? Approximately how long does it take to reach terminal velocity? change? described in parts (a) and (b). (b) (2 points) Let's model drag with p 1.25 instead. How do the answers in part (a) aie

Answer 1