# 2250 - 3
# Monday September 11
# Computation sheet
# Example 2, section 2.3
> 25*ln(294.0/245);

                             4.558038920

> y:= t-> -245*t + 294*25*(1 - exp(-.04*t));

              y := t -> -245 t + 7350 - 7350 exp(-.04 t)

> v:= t -> 294*exp(-.04*t) - 245; 

                   v := t -> 294 exp(-.04 t) - 245

> solve(v(t)=0,t);   #find when max height 

                             4.558038920

> y(4.558038920); #max height

                              108.280465

> solve(y(t)=0,t);  #find when returns to ground

                           9.410949931, 0.

> 9.410949931 - 4.558038920; #time descending

                             4.852911011

> v(9.410949931); #speed when it lands 

                             -43.2273093

# Conclusions:  bolt rises for 4.56 seconds, to a height of 108.3
# meters.  Then it spends 4.85 seconds descending,  landing with a
# velocity of -43.3 meters per second.
> with(plots):
Warning, the name changecoords has been redefined

> z:= t->-4.9*t^2 + 49*t;

                                       2
                       z := t -> -4.9 t  + 49 t

> plot({z(t),y(t)}, t = 0..10, color=black);

>