Challenge Problem #9 (a) Show that a point on the surface of the earth at latitude 0, relative to the equator has an acceleration of magnitude 3.37 cm/scos(0) relative to a reference frame not rotating with the earth. What is the direction of this acceleration? (b) Discuss the effect of this acceleration on the apparent weight of an object near the surface of the earth. (c) The free-fall acceleration of an object at sea level measured relative to the earth's surface is 9.78 m/s at the equator and 9.81 m/s at latitude 0 = 45. What are the values of the gravitational field g at these points?