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: 2.5 km 45° north of west; then 4.70 km 60° south of east; then 5.1 km straight east; then 7.2 km 55° south of west; and finally 2.8 km 10° north of east. What is his final position relative to the island? km o south of east

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

Consider the following vectors: A = 5.2j;  B = -4.1i + 2.5j.  Draw a diagram showing the addition of vectors A and B. (a) Find A + B in the Cartesian (x and y component) form. (b) Find the magnitude of A + B. (c) Find the direction of A + B, expressed as a polar angle. (d) Find 1.5A - 3.2B in the Cartesian (x and y component) form. (e) Find the magnitude of 1.5A - 3.2B. (f) Find the direction of 1.5A - 3.2B, expressed as a polar angle.   Note: New drawing also with solution

In the sport of orienteering, participants must plan carefully to get from one checkpoint to another in the shortest possible time. In one case, starting at a particular checkpoint, Sam decides to take a straight path that goes west for 500 meters, and then go northeast for 500 meters on another straight path to reach the next checkpoint. Northeast, by the way, means 45 degrees to both north and east. Between the same two checkpoints, Mary decides to take the shortest distance between the two checkpoints, traveling off the paths through the woods instead. (a) What is the distance that Mary travels between the checkpoints? (Note that Sam travels a total distance of 1000 m, although his speed is probably significantly higher than Mary's.) 387.30 V m (b) In what direction does Mary go? Specify her direction as a positive angle, measured counterclockwise from east. 22.5

A hiking girl needs to go 39.2 km straight North to get to base camp, instead the compass confuses her and she travels 17.248 km at a 3.9° deflection East from straight North.  Then she realizes what she has done and so guesses an angle of 17.8° deflection West of straight North and then hikes 30.576 km.  What is the magnitude of her displacement from where she is now located to base camp. (put your answer is standard units)

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

Gabby works as an aerial photographer. On one trip she takes off from the airport and flies 52km on a bearing N46°E. She then turns and flies for 43km until she is due east of the airport. How far is Gabby from the airport when she is due east of it? Is there more than one answer, explain.

A commuter airplane starts from an airport and takes the route shown in Figure P3.19. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.

A ship sets out to sail to a point 142 km due north. An unexpected storm blows the ship to a point 130 km due east of its starting point. (a) How far and (b) in what direction (as an angle from due east, where north of east is a positive angle) must it now sail to reach its original destination?