Question

A spherical capsule is to be released from rest at time 1-0 from a high altitude. The velocity of the capsule as a function of time is given by where g 9.81 m/s" is the gravitational acceleration constant and ca=0.25 kg/m is the drag coefficient. You are to use the false-position root-finding method to approximate the mass m of the capsule such that at time 11 = 10 s the speed of the capsule is vi = 12.2 m/s. Implement the false-position method. Use a=0 kg and b = 20 kg as you initial bracketing values. Perform iterations until your approximation comes to within 0.1 gram of the true value.

Answer 1

The Problem is solved in an appropriate procedure, i am attaching the steps used to solve it.

As per the solution the Iteration are performed and true values lies between 5 Kg to 20 Kg.

The values provided in the problem are: - g= 9.81 m/se (d = 0.25 kg/m t = 10 sec Speed V, = 12.2 ml As we know late through Weight = mass x g (acceleration due to gravity) As weight differs between an and by lets cale average weight (ath) 2) Wz ot20 - 10 kg. . mass (m) = g = 9.81 m/s² = 0.981. i Velocity - 50 981 x 9.81 tanh (Ja 81x0 25 x 10 ) 0. 25 0.981 - 6.204 x 0.0875 20.54285 lowing iterations the true Value Comes in beturen ska to 20kg,