Bukhovtsev-et-al-Problems-in-Elementary-Physics

MECHANICS 41
165. A body is thrown into a river from a steep bank with
a height H. The initial velocity of the body forms an angle (X
with the horizon and is equal to v•. At what distance from the
bank will the body fall? In how many seconds will the body
be at a height h above the water after motion begins? What is
the velocity of the body when it falls into the water?
166. At what angle to the horizon should a stone be thrown
from a steep bank for it to fall into the water as far as p0ssible
from the bank? The height of the bank h o = 20 metres and
the initial velocity of the stone V o= 14 mt«.
187. Two bodies are thrown at the same time and with an
equal initial velocity V o from point x = y = 0 at various angles ~
and (x, to the horizon (Fig. 62). What is the velocity with which
the bodies move relative to each other? What will the distance
between the bodies be after the time '( elapses?
188. A dive-bomber drops a bomb from a height h at a distance
I from the target. The speed of the bomber is e. At what
angle to the horizon should it dive?
169. Alassenger car is driving over 8 level highway behind
a truck. stone got stuck between double tyres of the rear
wheels of the truck. At what distance should the car follow the
truck so that the stone will not strike it if it fties out from
between the tyres~ Both vehicles have a speed of 50 km/h.
170. A ball freely falls from a height h onto an inclined plane
forming an angle cz with the horizon (Fig. 63). Find the ratio
of the distances between the points at which the jumping ball
strikes the inclined plane. Consider the impacts between the ball
and the plane to be absolutely elastic.
171. Find the acceleration of body A which slides without
initial velocity down a helical groove with a pitch h and a radius
R at the end of the n-th turn (Fig. 64). Disregard friction.
172. Two steel slabs M and N with a height h are placed on
sand (Fig. 65). The distance between the slabs I = 20 em. A ball
whose velocity has not been determined exactly moves over
slab M. It is only known that this velocity ranges between
200 cmls and 267 em/s.
(1) At what height h is it impossible to predict the horizontal
direction of the velocity of the ball at the moment when it
falls onto the sand? (Before it touches the sand, the ball strikes
slab N at least once.)
(2) At what minimum height of the slabs is it impossible to
predict the spot on section I which the ball will strike? Dlsre-