3. (Dynamics and Energy) A rollercoaster car of mass 100.0 kg starts at the top of a hill, and is pushed by the theme park staff, giving it an initial speed of 5.0 m/s just as it drops from the top of the hill. The car rolls down on a track and gains speed, and has just enough speed to complete a circular loop with radius 15.0 m. a. Determine the centripetal force required at the top of the loop. [1 mark] b. Calculate the required speed at the top to complete the loop. [1 mark] c. Determine the total energy at the top of the circular loop. [1 mark] d. Find the required height of the hill. [2 marks]