How Can Understanding Displacement vs. Distance Help Solve Physics Problems?

[Girl@NCSU]

I've tried several problems similar to these where I could get the answer checked without locking me out of my homework attempts, but I'm not really understanding what to do at all here - any and all help would be appreciated.


An airplane flies 200 km due west from city A to city B and then 275 km in the direction of 31.5° north of west from city B to city C.
(a) In straight-line distance, how far is city C from city A?
km

(b) Relative to city A, in what direction is city C?
° north of west

(c) Why is the answer only approximately correct?


2.A figure skater glides along a circular path of radius 5.00 m.
(a) If she coasts around one half of the circle, find the magnitude of the displacement vector.
m

(b) If she coasts around one half of the circle, find what distance she skated.
m

(c) What is the magnitude of the displacement if she skates all the way around the circle?
m

3. A quarterback takes the ball from the line of scrimmage, runs backwards for 11.0 yards, then runs sideways parallel to the line of scrimmage for 21.0 yards. At this point, he throws a 60.0-yard forward pass straight downfield, perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?
yd

 

[PeterO]

I've tried several problems similar to these where I could get the answer checked without locking me out of my homework attempts, but I'm not really understanding what to do at all here - any and all help would be appreciated. An airplane flies 200 km due west from city A to city B and then 275 km in the direction of 31.5° north of west from city B to city C.
(a) In straight-line distance, how far is city C from city A?
km

(b) Relative to city A, in what direction is city C?
° north of west

(c) Why is the answer only approximately correct?


2.A figure skater glides along a circular path of radius 5.00 m.
(a) If she coasts around one half of the circle, find the magnitude of the displacement vector.
m

(b) If she coasts around one half of the circle, find what distance she skated.
m

(c) What is the magnitude of the displacement if she skates all the way around the circle?
m

3. A quarterback takes the ball from the line of scrimmage, runs backwards for 11.0 yards, then runs sideways parallel to the line of scrimmage for 21.0 yards. At this point, he throws a 60.0-yard forward pass straight downfield, perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?
yd

The emphasis/basis of these seems to be the distinction between distance covered and displacement.

Your displacement in the period 5:00 am yesterday to 5:00 am today was probably zero: - you were in your bed at both times, however the distance you covered during that 24 hour period was probably several kilometres at least.EDIT: and in each case draw a diagram of the situation!