You are watching Harry Potter on his flying broom. You impose a coordinate system so that the ground is the xy-plane. At precisely noon the sun is directly overhead and you note that the shadow made by the broom on the ground goes from the point P(1, 2, 0) to the point Q(3, 4, 0) (P corresponds to the backend and Q the front). The broom is tilted upward making a 30 angle with the horizontal.

1. Find the length of the broom

2. At noon, assume the front end of the broom is at a height of 25 feet.
Find the symmetric equations for the path of the front end of the broom

3. Give the parametrization of the line in terms of arc length (distance traveled since noon)

4. Assume Harry is traveling at a constant speed of 24 ft/sec. Find the parametrization of the motion in terms of t seconds after noon. How long does it take to reach a height of 500 feet?

5. Assume Gary is at rest at noon, then accelerates at a constant rate of 3 ft/sec^2. Find the parametrization of the motion in terms of t, seconds after noon. How long does it take to reach a height of 500 feet?