2.3-10: Prior to chute open, the velocity model is v'=-32-0.15v, v(0)=0. The distance model is y'=v(t), y(0)=10000. The answers are v(20) approx -202 and y(20) approx 7084. After chute open, the velocity model is w'=-32-1.5w, w(0)=v(20). The distance model is x'=w(t), x(0)=y(20). Some maple solving is required, or a graphing calculator with zoom, to find the answer t approx 326. =====maple example===== x:=t->7000+120*exp(-1.5*t)-21*t; solve(x(t)=0,t); # solve an equation for t 2.3-20: The model is v'=-g-r v^2, v(0)=160 where g=32 and r=1/800. This model is solved on page 101. Do not solve the model; use formulae (13), (14) page 101 with v0=160, g=32, rho=1/800. The symbol y(t) is the height of the bolt measured from the ground, so y(0)=0. Ans published in the BOB are correct. 2.3-22: The model is v'=-g+r v^2 where g=32 and r=0.075 (page 102). Because the parachutist bails, v(0)=0 and y(0)=10000=y0, where y(t) is the distance from the ground. Page 102 requires v(t)<0, which means y'(t)<0 or y(t) decreasing. Opposite coordinates in which y(t) increases and measures the distance from the plane would require a different model, not found on page 102. Use formulae (17), (18) to answer the questions. Do not solve the model; that is done on page 102. Formula (17) gives 0=y0-(1/r)ln(u(t)) where y0=10000, r=0.075, u(t)=cosh(c2-t sqrt(rg))/cosh(c2). Solve for t to find the flight time. The terminal velocity is given by (18). maple ======= cosh(u) is the hyperbolic cosine, defined by cosh(u)=(exp(u)+exp(-u))/2 sinh(u) is the hyperbolic sine, defined by sinh(u)=(exp(u)-exp(-u))/2 tanh(u)=sinh(u)/cosh(u) arctanh(u) is defined by arccosh(cosh(x))=x Similarly for arcsinh, arccosh. u:=t->cosh(c2-t*sqrt(rho*g))/cosh(c2); eq:=10000 = (1/rho)*ln(u(t)); solve(eq,t); # solve an equation for t