154 Aptitude Test Problems in Physicsthe ball is v u (the axis of motion is directed
along the motion of the ball) in the reference frame
fixed to the foot of the player. After the perfect-
ly elastic impact, the velocity of the ball in the
same reference frame will be —(v u), and its ve-
locity relative to the ground will be —(v u) —
u. If the ball comes to a halt after the impact,
v + 2u = 0, where u = —v/2 = —5 m/s. The mi-
nus sign indicates that the foot of the sportsman
must move in the same direction as that of the
ball before the impact.
1.52. Since in accordance with the momentum
conservation law, the vertical component of the
velocity of the body-bullet system decreases after
the bullet has hit the body, the time of fall of the
body to the ground will increase.
In order to determine this time, we shall find
the time t 1 of fall of the body before the bullet
hits it and the time t 2 of the motion of the body
with the bullet. Let to be the time of free fall of
the body from the height h. Then the time in which
the body falls without a bullet is t 1 =
tonlY. At the moment the bullet of mass M hits
the body of mass m, the momentum of the body is
directed vertically downwards and is
MP= Mgto