Differential Equations Problem Solutions

Each solution provided below is not necessarily the only possible solution.  If a solution differs greatly from yours, copy and paste it from your browser to your Maple worksheet, then execute it and see if the final answers differ.

(1)  -2/5 m/s  (The initial height is not relevant.)

restart;
Newt_eq := F[net] = Drag - Weight;
F[net] := mass*diff(v(t),t);
mass := 2;
Drag := -50*v(t);
Weight := mass*10;
diff_eq := F[net]-Drag = -Weight;
dsolve({diff_eq,v(0)=-4},v(t));
odetest(%,%%); # a check
terminal_vel := limit(rhs(%%), t=infinity);

(2)  The drums are likely to crack.

Let 0 m be at ocean level and downwards be the negative direction in the coordinate system.

restart;
Newt_eq := F[net] = Drag + Buoy - Weight;
Drag := -1.17*v(t);
Buoy := 2092;
Weight := 2346;
F[net] := mass * diff(v(t),t);
mass := evalf(Weight/10);
diff_eq := F[net]-Drag = Buoy-Weight;
dsolve({diff_eq,v(0)=0},v(t));
odetest(%,%%); # a check
vel := unapply(rhs(%%),t);
terminal_vel := limit(vel(t),t=infinity);
pos := int(vel(t),t);
solve( -350 = pos, t);
vel(%[1]);

Differential Equations Problem Set

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