A ladybug is trying to get to a certain flower by following this path. She moves 23 cm to the left, then moves 33 cm at 35.3 degrees North of West (N of W) and then reaches the flower by moving 12 cm at 22.4 degrees North of East (N of E). What is the magnitude of her final displacement?

I start walking. The 1st leg of my trip I walk dA = 130 m at θA = 19° south of east. The 2nd leg of my trip I walk dB = 55 m at θB = 13° north of east. On my final leg I walk dC = 95 m at θC = 69.5° north of west. Choose the coordinate system so that x is directed towards the east, and y is directed towards the north. a) Write an expression for the x-component of the final displacement in terms of the given quantities. b)Write an expression for the y-component of the final displacement in terms of the given quantities. c) What is the magnitude of my displacement vector (in meters) as measured from the origin? d)  What is the angle of my displacement vector as measured counterclockwise from the +x-axis?

You are lost at night in a large, open field. Your GPS tells you that you are 100 m from your truck, in a direction 50.0o west of south. You walk 50.0 m due west along a ditch.  How much farther must you walk to reach your truck?

A diver explores a shallow reef off the coast of Belize. She initially swims d1 = 74.3 m north, makes a turn to the east and continues for d2 = 183.7 m, then follows a big grouper (a kind of fish) for d3 = 73.3 m in the direction θ = 43.9° north of east. Finally, she swims d4 = 193.4 m south.What is the straight-line distance between her initial and final positions in m?

At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 9.50 yards, back (in the −x-direction), then 15.0 yards parallel to the y-axis (in the −y-direction). He then throws the football straight downfield 60.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball?   What if? The receiver that catches the football travels 60.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run?

A jogger travels a route that has two parts. The first is a displacement A of 2.65 km due south, and the second involves a displacement → B that points due east. The resultant displacement A + B has a magnitude of 4.75 km. (a) What is the magnitude of B, and (b) what is the direction of A + B as a positive angle relative to due south? Suppose that A - B had a magnitude of 4.75 km. (c) What then would be the magnitude of B, and (d) what is the direction of A - B relative to due south? (a) Number i (b) Number i (c) Number i (d) Number i Units Units Units Units > > >

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?

Suppose a person walks so that their displacement is represented by a vector that has a magnitude of 52m (vector A). The direction of that initial displacement is 31 degrees north of east. After that, the person then walks 15 m due west (vector B).  Use trig to calculate the east and north components of the first displacement, vector A.

A football player runs for a distance d1 = 7.17 m in 1.08 s, at an angle of θ = 41 degrees to the 50-yard line, then turns left and runs a distance d2 = 10.66 m in 1.62 s, in a direction perpendicular to the 50-yard line. The diagram shows these two displacements relative to an x-y coordinate system, where the x axis is parallel to the 50-yard line, and the y axis is perpendicular to the 50-yard line.What is the magnitude of the total displacement, in meters? What angle, in degrees, does the displacement make with the y axis? (Note that the angle θ was given as measured from the x axis rather than the y axis.) What is the magnitude of the average velocity, in m/s? What angle, in degrees does the average velocity make with the y axis? (Note that the angle θ was given as measured from the x axis rather than the y axis.)

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?