romeoandjuliet

=ROMEO AND JULIET<33=

Introduction:
In this problem, Romeo has a ladder 30cm long which he wants to use to climb up to Juliet's window. However, when he holds the ladder flush against the vertical wall, the top of the ladder is too high by 3cm. If he moves the base of the ladder out and away from the wall, the top of the ladder moves down. In this investigation, we are to determine how far Romeo will have to move the base of the ladder away from the wall so that the top will be lowered by 3cm and then be exactly at Juliet's window.

HMMMM. Around 7?
 * Estimation:** How far do you think Romeo will hvae to move the base of the ladder away from the wall so that the top will be lowered by 3 cm and then be exactly at Juliet's window?

Solution:
This problem can easily be solved by drawing/looking at diagrams; we know that y = 3 because the question tells us that the ladder is too high by 3cm. Therefore 30-y must 27cm. we also know that the ladder is 30cm (this length is unchangable) we also know that the base and the wall make a 90° angle so we can use pythagoras theorem to write the equation; x = sqrt 30² - 27² so x = 13.077, when x is the the distance between the bottom of the ladder and the wall.

ORStart with the ladder positioned vertically against the wall (x=0, y=0). Progressively lower the ladder (y) by moving the base of the ladder away from the wall (x). Measure "x" and "y". Do this at least every 2cm, so that you will have more than fifteen data points. End with the ladder lying flfat along the floor (x=30, y=30) Note that the height of the top of the ladder will be (30-y)cm.

Enter your data for "x" and "y" into lists on your graphing calculator (L1 and L2). Also enter the values for (30-y) into L3, by using L3 = 30 - L2.


 * **x** || **y** ||
 * **2** || **29.93** ||
 * **4** || **29.73** ||
 * **6** || **29.39** ||
 * **8** || **28.91** ||
 * **10** || **28.28** ||
 * **12** || **27.495** ||
 * **14** || **26.53** ||
 * **16** || **25.38** ||
 * **18** || **24** ||
 * **20** || **22.36** ||
 * **22** || **20.39** ||
 * **24** || **18** ||
 * **26** || **14.967** ||
 * **28** || **10.77** ||
 * **30** || **0** ||

Using STAT PLOT, make a scatterplot of L1 against L2 and L1 against L3.


 * What is the shape of the graph? If you continued the graph, what complete shape would it make?**

If we continued this graph, the graph would look like a circle. Since the numbers are sq. rooted, the shape would be a circle. Although with our data, it would only be a quarter of a circle. If you want the whole circle, it can't be a 'real' function because there would be two identicals x's.

The Y = equation would be




 * Conclusion:

The data we modeled was perfect to the equation we made through methods of algebra. WE WIN. GG AVANI**