- #1
hastings
- 80
- 0
an object with mass m=0.1kg is thrown with an initial velocity v0=20m/s in a viscous matter that exercises a resistant force of F=-Bv (B=2kg/s and v=velocity). ignoring the gravity force, find the distance covered by the object in the viscous medium.
I tried this
F=-Bv=ma => a=(-Bv)/m;
a=(dv)/dt => dv/dt=(-Bv)/m --> v dv=(-Bv)/m *dt
integrating I get
[tex]-\frac{B}{m}t=\log v - \log 20[/tex]
since ds/dt=v
[tex]v=e^{-\frac{B}{m}t + \log 20}[/tex]
then integrate again [tex]\int{ds}=\int {e^{-\frac{B}{m}t + \log 20}dt[/tex]
I tried this
F=-Bv=ma => a=(-Bv)/m;
a=(dv)/dt => dv/dt=(-Bv)/m --> v dv=(-Bv)/m *dt
integrating I get
[tex]-\frac{B}{m}t=\log v - \log 20[/tex]
since ds/dt=v
[tex]v=e^{-\frac{B}{m}t + \log 20}[/tex]
then integrate again [tex]\int{ds}=\int {e^{-\frac{B}{m}t + \log 20}dt[/tex]