The velocity v(t) of an object with mass m = 68.1 kg in free fall at...

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The velocity v(t) of an object with mass m = 68.1 kg in free fall at time t is given by the following expression v(t) = mg (1-exp(-ct/m)) where g = 9.81m/s² and the drag coefficient is c. At time t = 10 sec, the velocity of the object is measured as 40 m/s and we wish to use this mea- surement to estimate the value of the drag coefficient c. Note that c = 0 is a degenerate solution which is not useful in this case. (a) Write down an expression f(c) such that the solution of the equation f(c)=0 with respect to c yields an estimate of the value for the drag coefficient using the measurement made above. [10 marks] c=u. (b) Describe the method of bisection for finding the roots of a function f(x). Why is this called a 'bracketing' method? [10 marks] (c) Write a snippet of code in the Matlab language that implements the method of bisection for solving f(c) = 0 above. Use variables c_u, c_1 to indicate the upper and lower bounds, respectively, for the estimate of the root. Initialise the bracket using values c_u = 16 and c_1 = 14 and terminate your iterations when cua| ≤0.01. You can assume that the function myfunc (u) returns the value of your function f(c) above at [10 marks] The velocity v(t) of an object with mass m = 68.1 kg in free fall at time t is given by the following expression v(t) = mg (1-exp(-ct/m)) where g = 9.81m/s² and the drag coefficient is c. At time t = 10 sec, the velocity of the object is measured as 40 m/s and we wish to use this mea- surement to estimate the value of the drag coefficient c. Note that c = 0 is a degenerate solution which is not useful in this case. (a) Write down an expression f(c) such that the solution of the equation f(c)=0 with respect to c yields an estimate of the value for the drag coefficient using the measurement made above. [10 marks] c=u. (b) Describe the method of bisection for finding the roots of a function f(x). Why is this called a 'bracketing' method? [10 marks] (c) Write a snippet of code in the Matlab language that implements the method of bisection for solving f(c) = 0 above. Use variables c_u, c_1 to indicate the upper and lower bounds, respectively, for the estimate of the root. Initialise the bracket using values c_u = 16 and c_1 = 14 and terminate your iterations when cua| ≤0.01. You can assume that the function myfunc (u) returns the value of your function f(c) above at [10 marks]