Part A You work for an environmental agency and residents of a rural area have occasionally seen what they think is a cougar in nearby farmers' fields. You have been asked to investigate the area and see if you can find and follow the cougar's tracks to get an idea of its location and the extent of its range. It takes a few days, but finally one morning you find fresh tracks near one of the farms you follow. You move at a brisk pace of 1.4 m/s in the direction N25E following the tracks. After 2 hours, you notice that the tracks change direction and move in the direction N70W. You continue following the tracks along this new heading travelling a little faster at 1.8 m/s. After 1.5 hours, you come to a river and the tracks disappear. You have confirmed that there is a cougar in the area. Your agency has asked you for the following:

1. Draw a vector diagram showing the distance and direction you travelled, as well as the resultant from your initial position to where the tracks disappeared at the river.

2. Determine the distance and direction of the resultant. You can use either of the methods you have learned in making your calculations.

Part B Abby and Ben meet in a local park at the edge of a large circular pond. They walk in opposite directions around the edge of the pond. Abby walks at a speed of 4.5 feet/second clockwise for 15 seconds, while Ben walks at a speed of 1.6 m/s counterclockwise for 12 seconds. When they stop, they look at each other and wave. Just then, they notice their other friend Carlie on the other side of the pond. Carlie estimates the angle between Abby, herself, and Ben, ACB, to be 42.

1. Set up a labelled diagram to model this scenario. (4 marks)

2. Determine the distances walked by Abby and Ben, and the distance around the pond between them. (8 marks)

3. What is the angle between Abby, the centre of the pond, and Ben? (2 marks)

4. How far are Abby, Ben, and Carlie from the centre of the pond? (4 marks) Show all your calculations and include a diagram with your solution. Please show all the work