Why does retrograde motion of the planets happen? a: the planets speed up and slow down at random times during their orbit. b: mars follows an orbital path with occasional loops in it. c: every planet farther from the sun than the earth orbits faster than earth. d: earth's rotation rate changes as the force of gravity from the sun varies. e: when earth overtakes a planet in its orbit, the planet will appear to move backwards for a short time.

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.