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I'm slightly stuck with an approximation of tmax, the time at which a ballistic projectile reaches maximum height. (projectile shot straigh upwards, no x motion)

So, by integrating the motion equation

m * dv/dt = -mg -bv

(where b is an air drag constant) I've created:

v(t) = (u + mg/b)*e^(-bt/m) - mg/b

which at tmax (t at maximum height) must be zero, which then gives:

tmax = (-m/b) ln [ (mg/b) / (mg/b + u) ]

where u is the initial velocity in y

Now whenm >> b*tmax, tmax = u/g, howver, I can't get that!

all I get is (using e^x = 1 + x + x^2/2! +...):

tmax = u / (mgb/bm + ub/m)

thanks for any help!

-tschew

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# Approximating ballistic motion.

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