A scout navigates an open terrain. He travels 50 m to the east, then 120 m to the north, then 30 m to the southwest. How far and in what direction should he travel in order to get back to his origin?

A robot is programmed to go 3.0 m south and then 1.0 m east and then 4.0 m northwest. How far does the robot need to travel to get back to its original position?

An airplane pilot wishes to fly directly westward. According to the weather bureau, a wind of 75.0 km/hourkm/hour is blowing southward. The speed of the plane relative to the air (called the "air speed") as measured by instruments aboard the plane is 310 km/hourkm/hour . In which direction should the pilot head? a)What is the speed of the air relative to a person standing on the ground, vA/G? What is the speed of the plane relative to the air, vP/A?

The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 44.0 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 26.0 km/h. How far from Grand Bahama is the hurricane 4.00 h after it passes over the island?

A driver leaves a 3 m board on a trajectory that takes her 2.5 m above the board and then into the Water 2.8 m horizontally from the end of the board. At what speed and angle did she leave the board?

A field biologist is studying the migration patterns of northern gannets (a type of seabird). On one particularday, she records that they fly 5.0 km northeast, then turn toward to the south of east by 30 degrees and fly 4.0 kmin the new direction. How far north or south of their original position are the birds?

A plane flies 479 km east from city A to city B in 45.0 min and then 950 km south from city B to city C in 1.10 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east).

A quarterback throws a football while standing at the very center of the field on the 50 yard line. The ball leaves his hand at a height of 5 ft and has initial velocity vo = 51i +37j + 27k ft/s. Assume an acceleration of 32 ft/s² due to gravity and that the i vector points down the field toward the endzone and the j vector points to the sideline. The field is 150 ft in width and 300 ft in length. Determine the position function that gives the position of the ball t seconds after it is thrown. The ball is caught by a player 5 ft above the ground. Assume the player is standing vertically with both toes on the ground at the time of reception. (Use symbolic notation and fractions where needed.) r(t): =

A plane flies 493 km east from city A to city B in 45.0 min and then 983 km south from city B to city C in 1.30 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east). (a) Number i Units (b) Number Units (c) Number i Units (d) Number i Units (e) Number Units II

A train at a constant 60.0 km/h moves east for 40.0 min, then in a direction 50.0° east of due north for 20.0 min, and then west for 50.0 min.What are the (a) magnitude and (b) angle of its average velocity during this trip?