Problem I. A total of 490 J of work is done on a pin when a 5.0-kg sledgehammer strikes it (bringing the sledgehammer to rest). Calculate the initial speed of the sledgehammer. (4 marks) Two common and identical carts are used to perform an experiment. Cart A is pushed toward the stationary cart B with a velocity of 2.6 m/s. After the collision, cart A bounces back with a speed of 0.8 m/s and cart B moves of with a speed of 3.4 m/s. Why is this not possible? Justify your answer with appropriate calculations. (4 marks) A 0.40-kg cue ball makes a glancing blow to a stationary 0.30-kg billiard ball so that the cue ball deflects with a speed of 1.2 m/s at an angle of 30.0 from its original path. Calculate the original speed of the cue ball if the billiard ball ends up travelling at 1.5 m/s. (5 marks) A child swings on a swing so that her centre of mass is located 2.4 m from the point where the rope is attached to the tree. If she swings so that her maximum amplitude causes the rope to make an angle of 47 with the vertical, calculate the child's maximum speed during the swing. (5 marks) A bullet with a mass of 45 g is fired into a 8.3-kg block of wood resting on a floor against a spring. This ideal spring (k = 76 N/m) has a maximum compression of 28 cm. What was the initial speed of the bullet? (6 marks)