
8.1.4.15 Geometric and physical applications
Problem:
A particle of mass \( m \) rises vertically with an initial velocity \( v_{0} \). Assuming air resistance is proportional to the square of the velocity of the particle (proportionality coefficient \( k>0 \) ), find the height of the ascent of the particle and the velocity, with which it will return to its original position, as well as the time of ascent and descent.
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