In the isentropic coordinate system (see section 4.6), potential temperature is used as the vertical coordinate. because potential temperature in adiabatic flow is conserved following the motion, isentropic coordinates are useful for tracing the actual paths of travel of individual air parcels. show that the transformation of the horizontal pressure gradient force from z to θ coordinates is given by

22. the top of a cliff is located a distance h above the ground. at a distance h/2 there is a branch that juts out from the side of the cliff, and on this branch a bird's nest is located. two children throw stones at the nest with the same initial speed, one stone straight downward from the top of the cliff and the other stone straight upward from the ground. in the absence of air resistance, which stone hits the nest in the least amount of time?