EXTENSION+(practical+applications)

One of the challenges in designing a sports stadium is to make sure that spectators can see the activities without their views being blocked by the spectators in front.

Your task is to design the tiered seating for a sports stadium. The back of each seat is 80cm behind the back of the seat in front, but raised up so that each row can see over the row in front. What factors do you think you will need to take into account when working out how high each seat needs to be?
 * Make some sketches showing what the cross-section (side view) of the seats might look like.** Will the seats lie on a straight line, or a curve? How steep?

All spectators must be able to see clearly a point 10m in front of the front row of seating: The spectator in the second row needs to have line of sight to the same point as the spectator in the first row, as seen in the diagram above. Notice that the spectator in the second row needs some extra clearance in order to see comfortably over the first spectator's head.

Here is a zoomed-in diagram: The first spectator's eye-level is 1.2m above the ground.

There is an extra 0.2m of clearance from his eye-level to the second spectator's line-of-sight. The second spectator is a further 0.8m away from the point on the pitch.
 * How high above ground level does spectator 2's seat need to be?**

Now draw a similar diagram with the dimensions and unknowns for spectators 2 and 3.


 * How high above ground level does spectator 3's seat need to be?**

Finally, imagine there were 40 rows of seating in the stadium.


 * Can you work out the heights above ground level of each of the 40 rows, and hence plot a side view of the seating?**

//It is very helpful to use a spreadsheet to perform the repeated calculations and plot the results.//

All working and calculations must be shown. When you start working on the 40 rows of seating you may use a spreadsheet to assist with the repeated calculations. Your submitted piece of work needs to include sketches, hand written working for the seat level two and seat level three, along with either all hand written working for the remainder of the stadium or a copy of the spreadsheet utilised with handwritten explanations of the formulas used in specific fields plus a scale diagram of the side view of the seating. It is preferred that you use a spreadsheet for the repeated calculations, if you need assistance using a spreadsheet please ensure you conference with me as soon as possible.