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Question: Throwing a ball with aire resistance

Question:Throwing a ball with aire resistance

maxwell 25 Maple
differential-equation dsolve
January 27 2017
1

I'm trying to plot the velocity of a ball thrown upwards with air resistance proportional to v^2 and also some simpler forms of this.

But the solution to v^2 returns root of and the plot stops for some specific time value. How can I proceed this plot to let's say 10 sec?

Staffan


 

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restart

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deq1 := m*(diff(v(t), t)) = -m*g:

``

sol := dsolve({deq1, v(0) = v__0}, v(t))

v(t) = -g*t+v__0

 (1)

V := unapply(rhs(sol), t):

``

``

``

deq2 := m*(diff(v2(t), t)) = -m*g-k*v2(t):

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sol2 := dsolve({deq2, v2(0) = v__0}, v2(t))

v2(t) = -g*m/k+exp(-k*t/m)*(v__0+g*m/k)

 (2)

V2 := unapply(rhs(sol2), t):

``

deq3 := m*(diff(v3(t), t)) = -m*g-k*v3(t)*abs(v3(t))

m*(diff(v3(t), t)) = -m*g-k*v3(t)*abs(v3(t))

 (3)

sol3 := dsolve({deq3, v3(0) = v__0}, v3(t))

v3(t) = RootOf(t+m*piecewise(_Z <= 0, arctanh(k*_Z/(k*m*g)^(1/2))/(k*m*g)^(1/2), 0 < _Z, arctan(k*_Z/(k*m*g)^(1/2))/(k*m*g)^(1/2))-m*piecewise(v__0 <= 0, arctanh(k*v__0/(k*m*g)^(1/2))/(k*m*g)^(1/2), 0 < v__0, arctan(k*v__0/(k*m*g)^(1/2))/(k*m*g)^(1/2)))

 (4)

V3 := unapply(rhs(sol3), t):

``

m := 0.258e-2:

``

plot([V(t), V2(t), V3(t)], t = 0 .. 5, color = [blue, red, black], gridlines = true)

  

``


 

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