Consider a situation in which Angie runs in the North direction along the straight edge of a lake (Y axis). Buddy starts out 50 metres to the east of Angie(x axis). They both start from rest. Angie runs at constant speed of u ms-1. Buddy notices angie and runs toward her at a constant speed v ms-1 in attempt to catch her. He changes direction every 2 seconds to notice angies new position. Buddy doesnt like to get wet and will avoid going into lake(-x axis)

1.Choose reasonable values for their running speed and fully justify your choices.
2.Construct a diagram to plot the positions and directions of both runners. Use trigonometry to find coordinates of points where buddy changes his direction.
3.determine recursive formulae for the x and y coordinates of buddy's position to establish discrete mathematical model
4.use spreadsheet or geometric software to simulate positions of runners for variety of values of speeds u and v, the time and distance
5.discuss conditions for buddy to catch up with angie
6. what limitations does it have when applied to other situations?