physics problems

1
Let the east direction be positive
A travels at 30 m/s
B travels at -20 m/s

Their speed difference is 30 - (-20) m/s
= 50 m/s

time = distance / speed
time = distance / speed difference of A and B
　　= 400 / (30+20)
　　= 8 s
Answer (1)


2
(a) Completely vertical means that a vector is parallel to the y-axis (if we express it on a coordinate plane) and has no component that leans towards the x-axis. A completely vertical vector is a vertical arrow, while a completely horizontal vector is a horizontal arrow (parallel to the x-axis).

(It will be easier for you to understand when a vector is on a coordinate system. A completely vertical vector is parallel to the y-axis, perpendicular to the x-axis. If the angle between the vector and the x-axis is not 90 or 180 degrees, the vector is not considered as a completely vertical vector. Vectors with degrees 0 ＜90, 90＜180, 180＜270, 270＜360 are not complete vertical or horizontal vectors. They have both vertical and horizontal components.)

(b)
...
since the 400N vector is completely vertical.. the horizontal component is 0 and the vertical component is 400N.

1.
Car A travel due east at 30m/s
Car B travel due west , or towards Car A at 20m/s
so to Car A , it seems Car B is travelling 50m/s towards it
(this is the concept of relative velocity)
time = distance / speed
time = 8sec
Answer (1)

2.
by the triangle law
any 2D vector can be broken into a x-component and a y-component
(in Amaths , we would express a vector in v = 3x+2y
to say it travel 3 unit left and then 2 unit upward , therefore it is a vector pointing up-left)
take a look at this : http://whyslopes.com/etc/CalculusAndBeyond/images/ch21c.gif

(a) "completely vertical" means this vector has no horizontal component , it is right angle to the horizon , therefore it has vertical component only
(b) by triangle law
....^ .......^
....| .......|
....| = ....| (vertial component) + . (horizontal component)
....| .......|