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PHYS 172 Problem Of the Week  Solution #2 (Spring 2012)
A falling rubber ball bounces off the floor. The velocity just before it hits the floor is
<2.7,−5.2,0> m/s. Just after it hits the floor, the ball’s velocity is <2.7,5.2,0> m/s (the
y axis is the vertical axis). The ball’s mass is 0.038 kg. The ball is in contact with the
floor for only 1.8 × 10
3
seconds.
(a) What is the vector change in momentum of the ball from just before to just after
it is in contact with the floor? Express your result as a vector.
Let us call the velocity just prior to hitting the floor
v
initial
and the velocity just after
hitting the floor
v
final
. Then we can express the change in momentum as:
(
)
0.038 (2.7
2.7),(5.2 ( 5.2)),0
0,0.40,0
/
∆ =

=

=
⋅

 
=
⋅
final
initial
final
initial
p
p
p
m v
v
kg m s
Alternatively, we could find the initial and the final momentum of the ball explicity
and then take the difference to find the change in momentum:
(0.038 2.7),(0.038
5.2),0
0.1026, 0.1976,0
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 Spring '08
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