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Problem 1 (60 points) datum M y = cos x, smooth track Figure 1: Fig. 1 shows a cart of mass M sliding on a smooth track y = cos z. The track starts at x = 0 and ends at x =. The cart is equipped with a propeller which exerts a thrust Fê, on the cart to keep the cart's speed in z direction a constant, i.e., = V₂ and V₂ = 0. Express all vectors in terms of i and 3. 1. Determine the position vector 7, velocity and acceleration a of the cart as a vector function of r and V₂, respectively (10 points).

Fig: 1