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

Solutions 119

wards relative to the middle of the car). Obviously,
a driving out is a driving in inversed in time.
Therefore, the car should be driven in a small gap
by backward motion.
1.14•. Let us consider the motion of the plane
starting from the moment it goes over to the cir-
cular path (Fig. 130). By hypothesis, at the upper
point B of the path, the velocity of the plane is
vl = v 0 /2, and hence the radius r of the circle
described by the plane can be found from the rela-
tion

2

4

= V 2 — 2a0 • 2r,

which is obtained from the law of motion of the

plane for h = 2r. At point C of the path where the

velocity of the plane is directed upwards, the total

acceleration will be the sum of the centripetal

acceleration a, =-- (vc 2 = 4 - 2aor, where ve

is the velocity of the plane at point C) and the

tangential acceleration at (this acceleration is

responsible for the change in the magnitude of the

velocity).

In order to find the tangential acceleration, let us

consider a small displacement of the plane from

point C to point C' Then = 4 - 2a^0 (r Ah).

Therefore, 4, - = —2a 0 Ah, where Ah is the

change in the altitude of the plane as it goes over

to point C'. Let us divide both sides of the obtained

relation by the time interval At during which this

change takes place:

Ve, — Vc^2  2

2a 0 Ah

At — At •

Then, making point C' tend to C and At to zero ,

we obtain

latvc = —2a 0 vc.

Hence at = —a 0. The total acceleration of the

plane at the moment when the velocity has the