James has just jumped out of an airplane. After he opens hisparachute he experiences 2 forces: the constant force of gravity,and a wind drag that is proportional to his velocity. His heightmay therefore follow the equation: d2h/dt2 =-9.8 - 2(dh/dt). As a second-order differential equation, this isnot technically solvable by separation of variables. However,because the variable h appears only in its derivatives, we can turnthis into a first-order equation, and solve that by separation.
a) Letting v = dh/dt, rewrite the above equation as afirst-order differential equation in v.
b) Your equation in part a suggests that there is one velocityfor which dv/dt = 0. What is this velocity?
c) Solve your equation using separation of variables. Yoursolution should contain an arbitrary constant: call itC1.
d) Calculate lim t to infinite v(t) and use it to describe whatis physically happening to James after he's been in the air for along time.
e) Now that you have a velocity function v(t), integrate it withrespect to t to find a position function h(t). This will introducea second constant C2.
f) Suppose James begins at a height of 3000m with no initialvelocity, what is his height 3s later?
