Mathematical calculations

Mathematical calculations

1) With respect to mathematical calculations why is it necessary to have all values used in a
calculation ,(containing more than one quantity),in the same unit system? What would be the
result if the quantities units were not all in the same system?
2) How do distances and displacements differ ?
3) What determines whether quantities are vectors or scalars ?
4) If an object in an open convertible moving at a constant 20mi/hr were thrown vertically upward,
where would it come down ?(neglect air friction)
5) If I go 50mi south, then 50mi east, and then 50mi north and I end up where I started out, where
am I ? 6) For some additional fun, consider the following: If a soccer player kicks a ball with a velocity of
15m/s at an angle of 60 degrees to the horizontal, at what time(s) in its flight will the ball have a
velocity with a direction of 45 degrees above or below the horizontal ?
7) Discuss one or more practical applications of Archimedes Principle in everyday life.