5.1 The solution for Re < 0.5
5.1 The solution for Re < 0.5
Clear[v,m,g,k]
vsolution1 =
DSolve[{m v'[t] == -m g - k v[t],v[0] == v0}, v[t], t]
Out[26]=
g m
--- + v0
g m k
{{v[t] -> -(---) + --------}}
k (k t)/m
E
We need to select the right hand side of the above replacement rule.
In[27]:=
velocity1 = vsolution1[[1,1,2]]
Out[27]=
g m
--- + v0
g m k
-(---) + --------
k (k t)/m
E
Now integrate to get y[t].
In[28]:=
Clear[v,m,g,k]
ysolution1 =
DSolve[{y'[t] == velocity1, y[0] == y0}, y[t], t]
Out[28]=
2
g m g m t m v0 m (g m + k v0)
{{y[t] -> ---- - ----- + ---- - -------------- + y0}}
2 k k (k t)/m 2
k E k
In[29]:=
Clear[v,m,g,k]
height1 = ysolution1[[1,1,2]]
Out[29]=
2
g m g m t m v0 m (g m + k v0)
---- - ----- + ---- - -------------- + y0
2 k k (k t)/m 2
k E k