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

116 Aptitude Test Problems in Physics

where g' = g cos a is the "free-fall" acceleration

in the coordinate system xAy, Thus,

vo sin2 op — a) = 2g1 cos a sin a.

Hence it follows, in particular, that if

< 2g1 cos a sin a = gl sin 2a

by hypothesis, none of the shell trajectories will

touch the shelter, and the maximum range Lmax

will correspond to the shell fired at an angle p =

n/4 to the horizontal. Here Lmax g.

If

vg > gl sin 2a

by hypothesis, the angle at which the shell should

be fired to touch the shelter will be

g1 sin 2a

=.(pt= a- F arcsin

vu

If, moreover, the inequality

vg

< sin 2a

vg-l- 2g1

is satisfied by hypothesis, which means that the
condition cpt ,> n/4 holds (prove this!), the angle

pat which the shell having the maximum range
should be fired will be equal to rt/4, and Lmax =
vlig. If, however, the inverse inequality
vg
von 2g1

> sin 2a

is known to be valid, which in turn means that

Pt < 71/4, we have

= (pt = + arcsin

v 2
Lmax = — - sin 2p

11g1 sin 2a

vc,

v 2

sin 2 ( a+ arcsin

gl sin 2a )

Do