The slender bar AB (IAB = 12 mL²) with a mass of mAB 20.0 kg and length of L = = 2.40 m, is supported by a pin at A, and is initially at rest. Ball C, with a mass of mc = 1.500 kg, strikes the bar with a velocity of vo = 40.0 m/s at 0.500 m above end B, as shown in Figure 1. The coefficient of restitution between the bar and the ball is e = = 0.600. Figure 1 C Vo 0.500 m A D Variables used: w' angular velocity of the bar immediately after impact VG' - velocity of the bar at its centroid immediately after impact velocity of the ball immediately after impact Vc 2.40 m VD' - velocity of the bar at point of impact with the ball at D, immediately after impact B 1) [20%] Determine the velocity of ball C immediately after impact, vč. 2) [20%] Determine the angular velocity of bar AB immediately after impact, w'. 3) [10%] 4) [10%] Determine the velocity of bar AB at its centroid immediately after impact, VG'. Determine the horizontal impulse at A. 5) [10%] Determine the vertical impulse at A. The inertia-force diagram for the slender bar AB is shown in Figure 2. A force F = 84.1 kN is acting 0. 500 m above end B. At this instant, the acceleration of the centroid of the bar aĠ in terms of its angular acceleration αAB is given as aG = aGx î+ 200 1 -αAB Ĵ. Figure 2 Ay A MABAGY G IABαAB MABAGX B A Ax G 2.40 m W F 0.500 m B 6) [10%] Determine the angular acceleration of the bar, αAB. 7) [10%] Determine the horizontal reaction force at A. 8) [10%] Determine the vertical reaction force at A.