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

Solutions

115

where n and k are integral and mutually prime

numbers. Substituting the values of t 1 and t 2 , we

obtain the relation between v, H, r, and a for

which the ball can "get out" of the well:

nr cos a

— k v

1.10. From all possible trajectories of the shell,

we chooLe the one that touches the shelter. Let us

analyze the motion of the shell in the coordinate

system with the axes directed as shown in Fig. 127.

Fig. 127

The "horizontal" component (along the axis Ax) of
the initial velocity of the shell in this system is
vox = vo cos (p — a), and the "vertical" compo-
nent (along the axis Ay) is vog = v 0 sin (( — a),
where p is the angle formed by the direction of the
initial velocity of the shell and the horizon tal.
Point C at which the trajectory of the shell
touches the shelter determines the maximum alti-
tude h' of the shell above the horizontal. Fig-
ure 127 shows that h' =1 sin a. The projection of
the total velocity v of the shell on the axis A y is
zero at this point, and
un 2
h' — "1/
2g"