- #1

Dragon M.

- 3

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## Homework Statement

I'm trying to compare the velocities at 5 meters of three projectiles subject to air resistance: the first with an initial velocity of 121.632 m/s, the second with an initial velocity of 136.8m/s, and the third at 182.442 m/s.

All three projectiles have a mass of 2.0x10^-4 kg (m), a cross sectional area of 2.81x10^-5 m^2 (A), and drag coefficient of .47 (C

_{d}). Density of air is assumed to be 1.204 kg/m^3.

## Homework Equations

The equation I have been primarily been using is the drag equation F

_{a}= 0.5Dv^2C

_{d}A

My initial plan was to use F = ma and V

_{f}^2 = V

_{i}^2 + 2a[itex]\Delta[/itex]x. However, I realized after doing these calculations that F

_{a}changes with respect to velocity.

## The Attempt at a Solution

This is my attempt to the solution of finding the velocity after 5 meters for 121.632 m/s.

F

_{a}= -(0.5)(1.204)(121.632 m/s)^2(.47)(2.81E-5) = -1.2E-1

Which I then realized that only applied initially at launch.

So I tried taking the derivative with respect to time.

dF

_{a}= (.47)(2.81E-5)(dv/dt)

I am fairly stuck at the moment. Where do I go from now? If there is not enough information,

**what information do I need**and what hints would you give to experimentally gain this information?