- Mechanics 13
the vertical direction? Assume that hail-
stones fall vertically.
1.12. A sheet of plywood moves over _a
smooth horizontal surface. The velocities of
points A and B are equal to v and lie in the
plane of the sheet (Fig. 3).
Determine the velocity of point C.
1.13. A car must be parked in a small gap
between the cars parked in a row along the
pavement.
Should the car be driven out forwards or
backwards for the manoeuvre if only its
front wheels can be turned?
1.14*. An aeroplane flying along the hori-
zontal at a velocity v 0 starts to ascend, de-
scribing a circle in the vertical plane. The
velocity of the plane changes with height h
above the initial level of motion according
to the law v 2 = v: — 2aoh. The velocity of
the plane at the upper point of the trajecto-
ry is vi = v 0 /2.
Determine the acceleration a of the plane
at the moment when its velocity is directed
vertically upwards.
1.15. An open merry-go-round rotates at an
angular velocity w. A person stands in it at
a distance r from the rotational axis. It
is raining, and the raindrops fall vertically
at a velocity vo.
How should the person hold an umbrella
to protect himself from the rain in the best
way?
1.16*. A bobbin rolls without slipping over
a horizontal surface so that the velocity v
of the end of the thread (point A) is directed