The perfect parachute

A parachutist of mass \(m\) jumps from height \(h\) and opening her parachute after \(t\) seconds. A retarding force given by \(\vec { F } =-k\vec { v } \) acts on her so that she lands on the ground with no velocity. Find \(h-\frac { 1 }{ 2 } g{ t }^{ 2 }\).

This problem is originally part of set Mechanics problems by Abhishek Sharma.

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