Answer:
2.408m/s
Step-by-step explanation:
To find the acceleration given to the tennis ball by the ground, we can use the following kinematic equation:
ℎ
=
1
2
�
�
2
h=
2
1
gt
2
Where:
ℎ
h is the height (in meters),
�
g is the acceleration due to gravity (which is -9.8 m/s^2 since it acts downward), and
�
t is the time (in seconds).
First, let's calculate the time it takes for the tennis ball to hit the ground from a height of 1.15 meters:
1.15
=
1
2
⋅
(
−
9.8
)
⋅
�
2
1.15=
2
1
⋅(−9.8)⋅t
2
Now, solve for
�
t:
�
2
=
2
⋅
1.15
9.8
=
0.2352
t
2
=
9.8
2⋅1.15
=0.2352
�
=
0.2352
≈
0.485
seconds
t=
0.2352
≈0.485 seconds
Now, the tennis ball rebounds to a height of 0.815 meters, so let's find the time it takes to reach that height using the same equation:
0.815
=
1
2
⋅
(
−
9.8
)
⋅
�
2
0.815=
2
1
⋅(−9.8)⋅t
2
�
2
=
2
⋅
0.815
9.8
=
0.1663
t
2
=
9.8
2⋅0.815
=0.1663
�
=
0.1663
≈
0.408
seconds
t=
0.1663
≈0.408 seconds
Now, we can calculate the time the ball was in contact with the ground:
�
contact
=
0.485
+
0.408
=
0.893
seconds
t
contact
=0.485+0.408=0.893 seconds
Now, we can find the acceleration given to the tennis ball by the ground using the formula:
�
=
2
ℎ
�
contact
2
a=
t
contact
2
2h
Where:
ℎ
h is the height to which the ball rebounds (0.815 m),
�
contact
t
contact
is the time the ball was in contact with the ground (0.893 s).
�
=
2
⋅
0.815
(
0.893
)
2
≈
2.408
m/s
2
a=
(0.893)
2
2⋅0.815
≈2.408m/s
2
So, the acceleration given to the tennis ball by the ground is approximately
2.408
m/s
2
2.408m/s
2
.