In the design of all-terrain vehicles, it is necessary to consider the failure of the vehicle when attempting to negotiate two types of obstacles. One type of failure is called hang-up failure and occurs when the vehicle attempts to cross an obstacle that causes the bottom of the vehicle to touch the ground. The other type of failure is called nose-in failure and occurs when the vehicle descends into a ditch and its nose touches the ground.

The accompanying figure, shows the components associated with the nose-in failure of a vehicle. In that reference it is shown that the maximum angle that can be negotiated by a vehicle when is the maximum angle at which hang-up failure does not occur satisfies the equation

Asincos+Bsin2-Ccos-Esin=0,

Where;

A=lsin1, B=lcos1, C=(h+0.5D)sin1-0.5Dtan1,

and E=(h+0.5D)cos1-0.5D

If l = 92 inch, h = 53 inch, D = 58 inch, and ₁ = 12.5 (0.21816 radians). Apply Newton-Raphson method to approximate the value of . Take a suitable initial guess of ₀ to start with and solve for 8 Iterations.

Part B:

For the equation in Part-A, develop a MATLAB code for Secant Method. Take suitable starting values and solve till 20 iterations. You may use Octave-online to develop and execute the code. Compare your results with the results obtained in part A.

D/2 B B