(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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.

3. 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 needand what hints would you give to experimentally gain this information?

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