A.) How fast is the coaster traveling at the bottom of the loop-de-loop. B.) Find the velocity of the coaster at the top of the loop-de-loop.
C.) Find the velocity at the end of the ride. (at 35 m)
D.) If a giant spring were placed at the end of the ride (35 m high), determine the spring constant necessary to stop the coaster in 1.8 m.
E.) If 60% of the original energy is lost due to friction, determine the velocity at the end. (35 m)

Emmy kicks a soccer ball up at an angle of 45° over a level field. she watches the ball's trajectory and notices that it lands, two seconds after being kicked, about 20 m away to the north. assume that air resistance is negligible, and plot the horizontal and vertical components of the ball's velocity as a function of time. consider only the time that the ball is in the air, after being kicked but before landing. take "north" and "up" as the positive ‑ and ‑directions, respectively, and use ≈10 m/s2 for the downward acceleration due to gravity.