One day, Sofia goes hiking at a nearby nature preserve. At first, she follows the straight, clearly marked trails. From the trailhead, she travels 2.00 miles down the first trail. Then, she turns 30.0° to the left to follow a second trail for 1.60 miles. Next, she turns 160.0° to her right to follow a third trail for 1.70 miles. At this point, Sofia is getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead her deeper into the woods. She would like to take a shortcut directly through the woods (ignoring the trails). What distance dsc does she have to walk to take a shortcut directly back to her starting point? Through what angle Osc should she turn to the right in order to take the shortcut directly back to her starting point? dsc = 0sc = miles

A hiking girl needs to go 24.8 km straight North to get to base camp, instead the compass confuses her and she travels 11.904 km at a 6.1° deflection East from straight North.  Then she realizes what she has done and so guesses an angle of 15.5° deflection West of straight North and then hikes 19.592 km.  What is the magnitude of her displacement from where she is now located to base camp. (put your answer is standard units)

The figure shows four vectors, A, B, C, and D, having magnitudes 8.0 m, 15.0 m, 12.0 m, and 4.0 m, respectively. The sum of these four vectors is 30° y B 30° X

A hiker walks 2.5 miles in a direction 65° West of North, then 3.5 miles in a direction 40° South of West, then 1.5 miles due South. What must be the vector displacement of the hiker during the fourth part of the trip in order for the resultant to be 5.5 miles due West for the entire trip? Drawing a vector diagram or drawing individual vectors will help.

An object moves in a circular path at a constant speed. What is the relationship between the directions of the object's velocity and acceleration vectors?  The velocity vector points in a direction tangent to the circular path. The acceleration is zero. The velocity and acceleration vectors are perpendicular. The velocity and acceleration vectors point in opposite directions. The velocity and acceleration vectors point in the same direction. The velocity vector points toward the center of the circular path. The acceleration is zero.

You walk 48.9 m to the north. You then turn 43.2 degrees to your right, so that you are facing 90-43.2 degrees north of east, and walk another 17.2 m. How far are you from where you originally started?

It takes a golfer three strokes to get a golf ball into a hole. On the first hit, the ball moves 6.0 m to the east. On the second hit, it moves 2.9 m at an angle of 20 ° north of east. On the third hit, it moves 0.50 m to the north. If the golfer had struck the ball directly into the hole in one stroke, what would have been the magnitude (in m) and the direction of the ball's displacement? Indicate direction as a positive angle measured counterclockwise from east.

In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: 2.50 km 45.0° north of west; then 4.20 km 60.0° south of east; then 1.50 km 25.0° south of west; then 5.30 km straight east; then 1.90 km 5.00° east of north; then 7.20 km 55.0° south of west; and finally 2.90 km 10.0° north of east. What is his final position relative to the island? (i.e., find the magnitude and direction of the displacement.) km at degrees South of East

First, a woman walks 25 m in a direction 49° north of east. Then she walks 23 m heading 15° north of east. Finally, she turns and walks 32 m in a direction 68° south of east. What is the total distance she covers? What is her total displacement?

Dr. B takes her dog ada on a walk. they start out heading south for 0.75 miles. then they turn left 30 degrees and they continue to walk for another 11 mile. Finally they turn right 9o degrees and they walk 1.9 miles. The whole walk takes 45 minutes.  What is the average speed of Dr.B and Ada on their walk? give your answer in m/s. What is the direction of the total displacement vector?