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

Solutions 155

The horizontally flying bullet hitting the body
will not change the vertical component of the mo-
mentum of the formed system, and hence the ver-
tical component of the velocity of the body-bullet
system will be

m m to

m+M u— m+111 g -1/.2 •

The time t 2 required for the body-bullet sys-
tem to traverse the remaining half the distance
can be determined from the equation

h , gt1

— --= uto-

2 2

This gives

t

to

_

1/m 2 + (m+M) 2 — m

1/.2 m+M

Thus, the total time of fall of the body to the

ground (M > m) will be

t. t° ilm2+(m+1/1)2+31 Alto -tr2.

ir2 m+M

1.53. In order to solve the problem, we shall use

the momentum conservation law for the system.

We choose the coordinate system as shown in

Fig. 159: the x-axis is directed along the velocity

vi of the body of mass ml, and the y-axis is directed

along the velocity v 2 of the body of mass m (^2).
After the collision, the bodies will stick together
and fly at a velocity u. Therefore,
rnivi =--- (m 1 + m 2 ) ux, m 2 v 2 = (m (^1) + m 2 ) uy•
The kinetic energy of the system before the collision
was
u =