QUESTION 1 (12 marks) Consider the diagram for question 1. A roller coaster car comes to the first hill (position X) at a speed of 3.15 m/s. The first hill of the roller coaster has a height of 37.1 m above the ground. The roller coaster car drops to position Y, which has a height of 10.6 m above the ground. Assume that mechanical energy is perfectly conserved as the roller coaster car falls from X to Y. The roller coaster track around position Y can be modelled using a circular shape. At position Y, a 55.9 kg person experiences a normal force of 2150[up]. At position Y, the person experiences two vertical forces: normal force[up] and gravity[down]. Calculate the radius of the circular track around position Y. QUESTION 2 (12 marks) A horizontal spring, of k : 14.3 N/m, is mounted at the edge of a lab bench to shoot marbles at targets on the floor 92.5 cm below. A marble of mass 8.41 grams is shot from the spring, which is initially compressed a distance of 4.17 cm. How far does the marble travel horizontally (in cm) before hitting the floor? Reminder: 1m 2 leacm 1kg 2 lOOOg QUESTION 3 (8 marks) Object i has an initial velocity of 6.0m/s[E] Object 2 has an initial velocity of 2.0m/s[E] Object 1 is travelling behind object 2 and they experience a rear-end elastic collision. After the collision, object 1 immediately comes to rest. a) What is be the velocity of object 2 right after the collision? b) If object 2 is 4.5kg, what is the mass of object 1? QUESTION 4 (8 marks) A 312 kg satellite currently orbits the Earth in a circle with radius 6.75x19A7m. The satellite must be moved to a new circular orbit of radius 8.52x107m. Calculate the additional total mechanical energy that the satellite requires. The mass of the Earth is 5.97xlOA24kg G is 6.67x10A-11NmA2/kgA2