Last night, a bottle hit a car's hood. Apparently, it was thrown out of a window in an apartment building due west of the car's location. The police are having difficulty determining which window the bottle came from, since the apartment has many windows, so they've called you in to help.

From the impact on the car, the police have determined that the bottle hit the car traveling 59 ft/sec. The angle of impact when viewed from above was 30 degrees north of west, and when viewed from the side was 37 degrees off vertical. Refer to the pictures below to understand the setting. Note: picture is not to scale



You will need to use some or all of these formulas in solving the problem:

• Distance moved horizontally by an object thrown with starting horizontal velocity $\displaystyle {v}_{{h}}$: $\displaystyle {d}={v}_{{h}}{t}$, where t is time measured in seconds. (Horizontal velocity remains constant)
• Distance moved vertically by a free-falling object (assuming initial vertical velocity of zero): $\displaystyle {d}={16}{t}^{{2}}$
• Velocity obtained by an object free-falling: $\displaystyle {v}_{{v}}={32}{t}$

Determine which window the bottle was thrown from.

The bottle was thrown from column (counting in from the left) and row (counting up from the bottom).

Write a report to the police summarizing your results, and how you determined your results. Be sure to state any assumptions made. This should be written in plain English, so that someone with very little mathematical background could still understand it. Feel free to be creative with your write-up.