Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

Fig. 134

124 Aptitude Test Problems in Physics

on 1 for the path between points A and B. The
graph is a segment of a straight line (Fig. 134).
The hatched area S under this segment is numer-

ically equal to the sought time. Let us calculate

this area:

IT

1/vi-pitv, 1 T ) (4_ 10

S -

2 2vi

/1— 2v111 la

since 1/v 2 = (1/v 1 ) / 2 /4. Thus, the ant reaches

point B in the time

4 m$— 1 ms

t —

2 x 2 m/s X 10-2 X 1 m

= 75 s.

1.22. Obviously, all the segments of the smoke trace

move in the horizontal direction with the veloc-

ity of wind. Let us consider the path of the loco-

motive in the reference frame moving with the

wind (Fig. 135). Points A' and B' of the smoke

trace correspond to the smoke ejected by the loco-

motive at points A and B of its circular path rela-

tive to the ground. Obviously, AA' II BB'. It can

easily be seen that the path of the locomotive

relative to the reference frame moving with the

wind is the path of the point of a wheel of radius R

rotating at a velocity vioc and moving against the

wind (to the left) at a velocity vw ind. This trajec-

tory is known as a cycloid. Depending on the ratio