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

112 Aptitude Test Problems in Physics

ponent of the initial velocity of the ball (the ball

does not strike the surface any more during the

time t). The height at which the ball will be in

time t is

a

Ah=ho +vo cos 2a • t-

2

gt

'

where vo cos 2a is the vertical component of the

initial velocity of the ball.

Since the ball starts falling from the height H

near the symmetry axis (the angle a is small), we

can assume that ho ae. 0, sin 2a = 2a, cos 2a n_s., 1,

Fig. 124

and s Ra. Taking into account these and other
relations obtained above, we find the condition for
the ball to get at the lowest point on the spherical
surface:

t=

(^8)
2gH sin 2a 2 }12gH
R 2 n
Ah vot—
gta R

2 = 2 — 16H
Hence H = R/8.
1.8. Since the wall is smooth, the impact against
the wall does not alter the vertical component of
the ball velocity. Therefore, the total time t 1 of