2.5+Crossing+the+Line

= =  =**__ Problem 2.5 & F.U __**=
 * // Pratik Sarkar //**
 * // Block-B //**
 * // Date-29/5/09 //**

1)
 * 1) Make a table showing the distance each brother is from the starting line at several different times during the first 40 seconds.**
 * Seconds || Emile || Henry ||
 * 0 || 0 m || 45 m ||
 * 5 || 12.5 m || 50 m ||
 * 10 || 25 m || 55 m ||
 * 15 || 37.5 m || 60 m ||
 * 20 || 50 m || 65 m ||
 * 25 || 62.5 m || 70 m ||
 * 30 || 75 m || 75 m ||
 * 35 || 87.5 m || 80 m ||
 * 40 || 100 m || 85 m ||

2)
 * 2) On the same set of axes, graph the time and the distance from the starting line for both brothers.**

3) The equation that we used for each brother are the the following listed below :-: Henri: y=2.5x Emile: y= x + 45
 * 3) Write an equation for each brother showing the relationship between the time and the distance from the starting line**

B) Emile will overtake Henri 76 meters away from the strating line becasue that is just after 30 seconds when both the brothers were at 75 mwters away from the starting line. And at the 31st second Henri is at 76 meters and Emile is at 77.5 meters.
 * B) How far from the starting line will Emile overtake Henri? Explain how you can use the table and the graph to answer this question.**

C) After 31 seconds Emile will overtakes Henri because at 30th second both the brother's were at 75 meters but at the 31st second Emile will be at 77.5 meters away from the starting line and Henri would be 76 meters away from the starting line.
 * C) After how many seconds will Emile overtake Henri? Explain how you can use the table and the graph to answer this question.**

Problem 2.5 F.U
1) After 3 seconds Henri would be ahead of Emile by 39.5 meters.
 * 1) After 3 seconds who will be ahead? By how much?**

2) When Emaile has already walked 10 meters, Henri would have walked 48 meters away from the origianl starting line.
 * 2) How far will Henri be from the starting line Emile has walked only walked 10 meters?**

a) I think that Emile's graph will be much more steeper than Henri's.
 * 3a) Which graph is steeper?**

b) For every change in value of x, y value will also change. The more the y value changes for the same amount of change in x value, the graph will be steeper. In this case we can see that Emile's graph will be steeper as for the same amount of change in x value, the change in value of y is much more than that of Henri's. For example if the equation is y=2x then the graph would not be as steep as in the equation y=5x which will create a steeper graph.
 * b) How can you determine which of the two lines will be steeper from their tables? From their equations?**

4)
 * 4) Explain how can you use the table, the graph and the equations to determine how far from the starting line each brother will be after 5 minutes.**

b) How can you predict where a graph will cross the y-axis from a table? From an equation?** a) Emile’s graph intersects with the y-axis at (0, 0) and Henri’s graph intersects with the y-axis at (0, 45). These points mean that Emile and Henri were at these particular points at zero seconds. b) We can predict that a graph crosses the y- axis simply by extrapolating the graph. For an equation, we need to put the value of x as 0. Then the value of y is calculated to know where the graph will intersect the y-axis. The graph with equaltions like x=2, will never cross the y-axis (it will be parallel to the y-saxis).
 * 5a) At what points do Emile and Henri's cross the y axis? What do these points mean in terms of race?

a) Copy and complete the table below to show Yuvett's distance from the starting line from 0 to 7 seconds. b) Which of the following gives the relationship between Yvette's distance from the starting line, d, and the time, t?** ii. d = 2+20 iii. d = 20t+2 iv. d = 20+t v. d = none of the above**
 * 6) Emile's friend Yvette joins the race. Yvette has a head start of 20 meters and walks at 2 meters per second.
 * i. d = 20+2t

a) **YVETTE'S WALKING DISTANCE**
 * Time (seconds) || Distance (meters) ||
 * 0 seconds || 20 meters ||
 * 1 seconds || 22 meters ||
 * 2 seconds || 24 meters ||
 * 3 seconds || 26 meters ||
 * 4 seconds || 28 meters ||
 * 5 seconds || 30 meters ||
 * 6 seconds || 32 meters ||
 * 7 seconds || 34 meters ||

b) It will be equation numer 1 which is x=20+2t