leviathanX777
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1. A particle moves vertically under gravity and a retarding force proportional to the square of its velocity. If v is upward or downward speed, shot that a = +/-g -kv^2, where k is a constant. If the particle is moving upwards, show that its position at time t is given by;
z = z0 +(1/k)lncos[rootgk (t0-t)] where z0 and t0 are integration constants.
3. I proved the a = +/-g -kv^2 but I spent almost an hour looking at the next part with no results. I integrated twice to get x(t) = -gt^2/2 - kv^2t^2/2 + z0 + t0
I have no idea what to do after this, I mean I don't know how you bring the cos into the problem. This hint is also given; lncosx = -1/2 ln(1 + tan^2x)
Cheers
z = z0 +(1/k)lncos[rootgk (t0-t)] where z0 and t0 are integration constants.
Homework Equations
3. I proved the a = +/-g -kv^2 but I spent almost an hour looking at the next part with no results. I integrated twice to get x(t) = -gt^2/2 - kv^2t^2/2 + z0 + t0
I have no idea what to do after this, I mean I don't know how you bring the cos into the problem. This hint is also given; lncosx = -1/2 ln(1 + tan^2x)
Cheers