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Problem 5: The trajectory of a roller coaster can be described by the following parametric equation F(0) = x(0)i+ y(0)j + =(0)k where x (0) = (a + bsin # ) cose y(@) = (a + b sin @) sin e (=(@) = b+ bcose a and b are constants. If e is a function of time, i.e. 8 (t), then the parametric equation described certain motion for a moving point along the trajectory. Let 8 (t) = wt where @ is constant. Find the tangent vector for this curve at any point on the curve, i.e. find the velocity of this moving dr point, v = = =? Hint: refer to example 6 in lecture $ notes. Problem 6: (Computer Exercise) Graph the parametric equation (roller coaster) given in Problem 5 using Maple Matlab. Assume that a = 200 and b = 150. Attach a print of your graph to this assignment. Sample code is given to graph the following helical or spiral curves using Matlab and Maple. "(t) = 3 costi+ 3 sintj + 20tk Graph using Matlab: % Parametric Equations for Spiral t = linspace(0, 10*pi,5000); *Total of 5 turns will be graphed for this spiral r = 3. ; c = 20 ; x = 3*cos(t) ; y = 3*sin(t) ; z = (*t ; comet3(x,y,z) ; plot3(x,y,z,'Color",'m','Linewidth',1) ; title({'Parametric Equations for Spiral';x=rcos\\ theta"; y=rsin\\theta";"z = c\\theta"}) ; Graph using Maple: Following Maple command can be used to graph the helical curve. with(plots): spacecurve([3*cos(t), 3*sin(t), 20*t], t=0..25, numpoints =500, axes=BOXED); Here the option "numpoints =500" defines how smooth the curve is. Attach you're a printout of the plot in the assignment