Question Solved1 Answer 19. Solve the problem.An object of mass m is dropped from a helicopter. Assuming that air resistance is proportional to velocity, the velocity v of the object satisfies the equation: du k + -0 = 9 dt Find velocity as a function of time t. m mg k em - em V = m mg (1) k kg (1-e e) mg (1 - e) U = k

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Transcribed Image Text: 19. Solve the problem.An object of mass m is dropped from a helicopter. Assuming that air resistance is proportional to velocity, the velocity v of the object satisfies the equation: du k + -0 = 9 dt Find velocity as a function of time t. m mg k em - em V = m mg (1) k kg (1-e e) mg (1 - e) U = k
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Transcribed Image Text: 19. Solve the problem.An object of mass m is dropped from a helicopter. Assuming that air resistance is proportional to velocity, the velocity v of the object satisfies the equation: du k + -0 = 9 dt Find velocity as a function of time t. m mg k em - em V = m mg (1) k kg (1-e e) mg (1 - e) U = k
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Given(dv)/(dt)+(k)/(m)v=g" it is "in the form of I diffeeluation,(dv)/(dt)+Q(t)v=P(t)Solution is,{:[AA(I*F)=int P(t)*(I*F)dt],[rarr(1)],[{:[" where, "],[I*F=" Integrating factrr "=e^(-rarr()theta(t)dt]:}],[=e^(int(k)/(m)dt)] ... See the full answer