Question1
As thermonuclear fusion proceeds in its core, the Sun loses mass at a rate of 3.64 109 kg/s. for the duration of the 5,000-yr period of recorded history, by how much has length of the year changed due to the loss of mass from the Sun? Assume the Earth's orbit is circular. No external torque acts on the Earth–Sun system, so angular momentum of Earth is constant.
Question2
One bright summer day a swimmer is floating with her head just above surface of a large lake where the water has index of refraction n = 1.38. Nearby she sees a tall wooden post emerging from the water. As she looks into the water at just the right angle she can see bottom of the post, that is embedded in lake bottom, a distance h = 5.60 meters below the water's surface. As she floats away from the post, finally she can no longer see the bottom of it. At what distance from post does this occur?