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I've been toying around with a cheap slingshot and some steel balls and cannot figure out how to calculate the velocity of the projectile at a given time/distance.

What I've done so far:

I derived a fairly accurate formula for the potential energy of the slingshot by measuring the pull force at several points and using my graphing calculator to integrate F(d) = 114.2d^0.678 from 0 to 0.5 meters find the total energy which is around 21 J.

I can easily find the initial velocity of the steel ball (assuming all other parts of the slingshot are massless), and calculate the force of air drag at that instant. However, I don't know calculus and cannot derive a formula that will give me the instantaneous acceleration or velocity with the ever decreasing drag. I've tried doing it without differential equations but the deceleration then turns out to be linear, which I don't think is correct.

I would really appreciate someone giving me a hand in this endeavor, because I've been reading calculus materials for the most part of today, but cannot seem to understand enough to enable me do solve my problem. Here is the data:

mass of ball - 0.0035 kg

sectional area - 7.088e-5 m2

KE - 21 J

air density - 1.125 kg/m3

Cd - 0.47

Also, could you tell me how to use differential equations with a TI-84 calculator

Thank you

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# Calculating velocity of a projectile accounting for drag

Can you offer guidance or do you also need help?

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