11. LO 8: Martin walks 2 km 45° east of south (Leg 1). He then changes directions and walks another 3 ° north of east (Leg 2). km What is Martin's displacement (magnitude and direction)? Use the graphical method. Now calculate Martin's displacement (magnitude and direction) using the analytical method. Think: How will you set up the problem? What quantities are given? What are unknown? What is asked to be found? Predict: What range should the magnitude of the resultant displacement be?

1. You have been hired to survey a new national park area. Youbegin at Point A on the map. You had originally planned to builda bridge from Point 1 to Point B, but have found the ground atPoint 1 is too unstable. So, you decided to build the bridge fromPoint A to Point B. You know the distance from Point A to Point 1is 30m. Within the AB1 triangle the angle at Point B is 45°, andthe angle at Point A is 20°.How long will the bridge need to be?2. You scout the territory northwest of B for 62m. You determineyou can build a flat trail here. This trail will end at point C. Usingan imaginary line due north from B you find the angle from B toC is 22°.How far north is Point C from Point B? 3. There is a hill at Point C, and you climb it to get an idea of whereto travel to next. You see the edge of a forest (Point D). Youclimb back down to the bottom of the hill (Point C) and walk toPoint D. You track your distance and find you have travelled98m. Using a tool you find the angle from Point D to…

Suppose you walk 23.5 m straight west and then 19m straight north for a total magnitude of 30m.  A. What is your displacement vector (in m)? Express your answer in vector form. Assume the +x-axis is to the east, and the +y-axis is to the north. B. What is the direction of your displacement ( in degrees counter clockwise from the x-axis)?

A car moves 4.0 km in a straight line in a direction 40º East of North. It then moves 7.0 km 20o South of East.   Sketch the trip as accurately as you can. Show the coordinate axes. Label all vectors. Show the resultant displacement. Use the analytical method to solve for the magnitude and direction of the resultant. Show all equations and steps in the calculations. Do the calculations match the graph you have drawn in part (A)?

1. Compute the x- and y-components of the vectors A, B, C, and D in Figure 1. 2. A postal employee drives a delivery truck over the route shown in Figure 2. Use the methods of components to determine the magnitude and direction of her resultant displacement.

The polar coordinates of a point are 4π/34π/3 and 5.50 m. What are its Cartesian coordinates? A trapper walks a 5.0-km straight-line distance from her cabin to the lake, as shown in the following figure. Determine the east and north components of her displacement vector. How many more kilometers would she have to walk if she walked along the component displacements? What is her displacement vector?

Directions: Using the component method, solve the following problems. Show your complete solutions. Express your answers in two decimal places.

Part AGiven the vectorsA⃗ and B⃗shown in the figure ((Figure 1)), determine the magnitude ofB⃗−A⃗.Express your answer using three significant figures. Part BDetermine the direction of B⃗−A⃗.Express your answer using two significant figures. Part CDetermine A⃗ − B⃗ without using your answer in parts A and B. Then compare your results and see if they are opposite. Determine the magnitude of A⃗−B⃗.Express your answer using three significant figures. Part D Determine the direction of A⃗ −B⃗ A→−B→. Express your answer using two significant figures.

1. Given: Vector D, with horizontal and vertical components: 20 in and 30 in, respectively. Vector D2 with horizontal component 20 in at 150° True north. Vector D3 is the displacement of an object which moved at 10 in/min for 4min due South. Reg'd: a. Draw the three displacements (D1 D2, D3) and the resultant displacement D in one Cartesian plane b. Determine the vertical and horizontal components of each displacement: Dıx Dry Dzx Dzy D3x Day c. Components of the resultant vector d. Magnitude of the resultant vector D e. Direction 0 of the resultant vector D

24. Suppose you get in your helicopter and you fly 10 mi in the direction of 205◦, and then you fly 30 mi in the direction of120◦.24a. Find your displacement.Note: your displacement is the vector that goes from your starting point to your ending point. It tells you how your positionchanged.24b. How far did you go?24c. What direction would you need to fly if you wanted to go back to where you started?25. A plane is flying through the air. If there were no wind, then the plane would be flying at a speed of 180 mph in thedirection of 40◦. But the wind is blowing at a speed of 25 mph in the direction of 80◦.25a. How fast is the plane going?25b. In what direction is the plane flying?