1. Suppose that Galileo fired a cannon in a horizontal direction from a height of 50 feet above level ground, and found that the cannon ball hit the ground 3000 feet away.
(a) What was the speed of the cannon ball when it left the cannon?
(b) How far would the ball have gone if it had been fired by the same cannon from a height of 200 feet?
(Ignore air resistance in answering this problem.)
2. Suppose that Snell found that the relation between the angle of inci- dence i and the angle of refraction r when a light ray passes from air to medium A is
sin i = 3
sin r
while when a light ray passes from air to medium B the relation is
sin i = 2 .
sin r
What is the relation between the angles of incidence and refraction when a light ray passes from medium A to medium B?
3. Suppose that all of Newton's laws were correct, except that the force of gravity decreases with the inverse cube of the distance, rather than the inverse square. What would replace Kepler's third law, for planets moving in circles with the Sun at the center?
4. Suppose that the largest distance of any point on an ellipse from the center of the ellipse is 1 meter, and the distance from one focus of the same ellipse to the other focus is also 1 meter. What is the shortest distance from the center of that ellipse to any point on the ellipse?
5. Suppose that if Copernicus could travel to the planet Bacchus, and look back at the Earth, he would see that the angle betwseen the lines of sight to the Sun and the Earth is never more than 20?. How far in Astronomical Units (AU) is Bacchus from the Sun? (You can take the orbits of the Earth and Bacchus to be circles, in the same plane, and with the Sun at the center of both.)