You are skiing down the slope of Mt. Aggie. Your path is described by equation: Y(X)...

    

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You are skiing down the slope of Mt. Aggie. Your path is described by equation: Y(X) = Acos(T) + A where d = 1000 and A = 300. Gravity (g) = 9.8 Velocity (tangential velocity) along the arc is simply the potential energy converted to kinetic energy: (X) = √2gh where h = 2A - Y(X) Tasks: For the interval x E (0,d): a. Plot skier velocity v(x) vs x. Does it match your intuition of the skier's speed? b. Find the equation and plot the radius of curvature p(x) vs. x c. Find the equations and plot the skier's tangential(a), normal (a.), & total (all) acceleration vs. x For the location xd/2: d. Find skier's velocity [v.: v.] and acceleration [a,; a,] in cartesian coordinates e. Find skier's velocity [v.: v.] and acceleration [a,; a,] in polar coordinates Discuss: f. What physical, operation and design considerations have we neglected in this example, and how would they affect the skier's motion? Think of shape, friction, etc. Explain in words. Ym) 0 200 400 OHY Xm) 600 800 1000 You are skiing down the slope of Mt. Aggie. Your path is described by equation: Y(X) = Acos(T) + A where d = 1000 and A = 300. Gravity (g) = 9.8 Velocity (tangential velocity) along the arc is simply the potential energy converted to kinetic energy: (X) = √2gh where h = 2A - Y(X) Tasks: For the interval x E (0,d): a. Plot skier velocity v(x) vs x. Does it match your intuition of the skier's speed? b. Find the equation and plot the radius of curvature p(x) vs. x c. Find the equations and plot the skier's tangential(a), normal (a.), & total (all) acceleration vs. x For the location xd/2: d. Find skier's velocity [v.: v.] and acceleration [a,; a,] in cartesian coordinates e. Find skier's velocity [v.: v.] and acceleration [a,; a,] in polar coordinates Discuss: f. What physical, operation and design considerations have we neglected in this example, and how would they affect the skier's motion? Think of shape, friction, etc. Explain in words. Ym) 0 200 400 OHY Xm) 600 800 1000