Given the following equation for the velocity of a skydive: v(t) = v(tt) + {g [C

Question

Given the following equation for the velocity of a skydive: v(t) = v(tt) +   {g   [C**A/2m] * [(v(tt)^)2]   }*t

note that v(tt) means the velocity is a function of time and the time step, NOT velocity times the difference of the time and the timestep

Where:

C isdrag coefficient = 0.581

A is cross sectional area - 1.035 m^2

is the density of air = 1.14 kg/m^3

g is gravity = 9.81 m/s^2

v is velocity

t is time

t is the time step, given as 0.1 seconds

m is the mass = 80 kg

initial velocity v(t=0)= 0

Write a program that asks for mass, cross sectional area, and drag coefficient, as well as how long to calculate the dive out to (for example, do you want the dive to last 10 seconds, 16 seconds, 25 seconds), and what the time step should be (0.1 sec)

As your program does its calculations, it should save the time and velocities in an array (i.e., in two separate one-dimensional arrays, one for time and the other for velocities). One you have calculated all these values, write the output to a le. The le should have two columns, the rst being the time (t) and the second being the velocity (v(t)) at that time. You can separate the two columns either by a space, tab, or comma Your program, then, should also prompt you for the output lename

Explanation / Answer

it mostly moves straight down in a stable position because of the angled sides. Also, when it is dropped from a reasonable height (like 2 meters) it will still reach terminal velocity. Finally, you can stack coffee filters and drop them. If you stack three filters, you effectively change the mass of the object but not the drag force parameters (shape and area).

But what is terminal velocity? I will answer this by considering a falling coffee filter. Suppose I let it drop from some height. Right after release, the coffee filter isn’t moving. Since it has a zero velocity, the drag force is also zero. The only force on the filter is the gravitational force (which is the mass multiplied by the gravitational field g) so that it accelerates down with an acceleration of -9.8 m2 (like any other falling object)

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