The motion of a bouncing basketball is monitored by a motion sensor'

1
The motion of a bouncing basketball is monitored
by a motion sensor.
The displacement S from the ground surface at
time t is measured.
velocity is V
basketball
At the instant t , displacement from O S
ground surface
O
2
The motion of the basketball in air between the
first and second rebound is studied.
3
The displacement S of the basketball from the
ground surface at time t is shown in the table.
S is recorded in 0.02 s time intervals.
For convenience the time instant is set to t 0
for the first set of data. The ball just clears
the ground surface at this instant.
4
The displacement S of the basketball from the
ground surface at time t is shown in the table.
S is recorded in 0.02 s time intervals.
At t 0.39 s , the basketball reaches its
maximum height of 0.732 m above the ground
surface.
5
The displacement S of the basketball from the
ground surface at time t is shown in the table.
S is recorded in 0.02 s time intervals.
At t 0.77 s , the basketball almost reaches
the ground surface again.
6
The displacement-time graph is shown below.
7
The time t and the displacement S are
measured by instruments.
How can we estimate the velocity of the
basketball by means of the time and displacement
data ?
8
Consider the displacement of the ball at the
instants t 0.22 s and t 0.24 s.
The average velocity within this time interval is
For a very short time interval, the velocity
obtained can be assumed to be the instantaneous
velocity at the instant in the middle of the time
interval.
Therefore we have V 1.55 m s-1 at t
0.21 s .
9
Consider the displacement of the ball at the
instants t 0.65 s and t 0.67 s.
The average velocity within this time interval is
For a very short time interval, the velocity
obtained can be assumed to be the instantaneous
velocity at the instant in the middle of the time
interval.
Therefore we have V -2.60 m s-1 at t
0.66 s .
10
If V is positive, the ball is rising up.
If V is negative, the ball is falling down.
11
The complete V-t table is obtained.
12
A velocity-time graph is then plotted.
It seems that, within limits of experimental
error, the graph is a straight line graph.
13
A velocity-time graph is then plotted.
A best-fit line is drawn.
14
A velocity-time graph is then plotted.
At t 0 when the ball just clears the ground
surface, the velocity of the ball is about 3.8
m s-1.
15
A velocity-time graph is then plotted.
At t 0.39 s, when the ball reaches the
maximum height, the velocity of the ball is 0 m
s-1. It is instantaneously at rest.
16
A velocity-time graph is then plotted.
At t 0.78 s, just before the ball reaches the
ground surface, the velocity of the ball is -3.8
m s-1. It has the same SPEED as it leaves the
ground surface at t 0.
17
A velocity-time graph is then plotted.
(0, 3.8)
The slope of the graph is
(0.78, -3.8)
The ball is moving with uniform acceleration. The
acceleration is the same either the ball moves up
or down.
The acceleration acts vertically downward.
18
Consider the complete velocity-time graph of the
bouncing ball
For all the sections corresponding to the ball
moving in air, they have the same slope, i.e.,
the same acceleration.
This is the acceleration due to gravity.