A layer of air has a temperature T0 of 30 Celsius at ground level and a lapse rate ? of 20 Celsius/km. A parcel originatiing at the surface is displaced upward with velocity v0 of 1 m/sec.
a) Ignoring friction and assuming dry adiabatic ascent, find expressions for the altitude z(t) and velocity v(t).
b) Find the time that it takes for the parcel to reach an altitude zf of 500m and determine its upward velocity at that point.