**Note: Mathematical Insights 4.3, 4.4 and 4.5 from the text are particularly useful.
**

**1. Evaluate the following expression: **

** **

**2. Evaluate the following expression: **

** **

**3. Let us play with the scale of the universe. Imagine that the solar
system has been shrunk to the size of a dinner plate, i.e. the diameter
of Pluto's orbit is now 20cm.
a. Look up the orbit of Pluto using the appendices of the textbook.
By what factor has the orbit been reduced to become only 20cm across? i.e.,
give the number you calculate when you divide the diameter of Pluto's orbit
by 20cm. **

**b. At that scale how big is:
i) a human?
ii) the radius of the Earth?
iii) the distance from the Earth to the Sun?
iv) the distance to the nearest star?
v) the distance to the center of the Milky Way?
vi) the distance to the nearest galaxy (M31)?
vii) the radius of the Universe? **

**Hint: Use information from the first two lectures and from the text
to get rough figures for the distances required. **

**4. We all watched in awe recently as NASA sent images back of the dwarf planet Pluto. For the spacecraft
to have reached its destination in seven years after launch, how fast must it have been travelling?**

5. A moon rocket is accelerating at 4 gees (40 m/s/s). It has mass of 10^{6} kg. How much force is the engine producing?

6. Two hockey players stand on a frictionless surface facing each other. One has mass of 100kg and the other has mass of 50 kg. The small one swings at the large one, his fist exerting 10 Newtons on his opponents nose for 0.1 seconds. The large fellow's nose returns the force equally (Newton #3). How fast is each moving after the encounter?

7. The largest star in our galaxy has a mass of 10^{32} kg. How long does it take a planet at 1 AU (1.5x10^{11} m) to orbit?

8. What velocity is required to escape from the solar system, starting at a distance of 1 AU from the Sun? (1AU = 1.5x10^{11}m= Sun/Earth Distance)