Respuesta :
Answer:
To solve this problem, we can use the equations of motion under constant acceleration due to gravity. Since the ball is dropped, its initial velocity is 0 m/s.
Time to hit the ground (ignoring air resistance):
We can use the equation for the displacement (s) of an object under constant acceleration:
�
=
�
�
+
1
2
�
�
2
s=ut+
2
1
at
2
Where:
�
s is the displacement (300.0 m, in this case)
�
u is the initial velocity (0 m/s)
�
a is the acceleration due to gravity (approximately
9.81
m/s
2
9.81m/s
2
)
�
t is the time taken
Rearranging the equation for
�
t, we get:
�
=
2
�
�
t=
a
2s
Substituting the given values:
�
=
2
×
300.0
m
9.81
m/s
2
t=
9.81m/s
2
2×300.0m
�
≈
600.0
m
9.81
m/s
2
t≈
9.81m/s
2
600.0m
�
≈
61.1737
s
2
t≈
61.1737s
2
�
≈
7.82
s
t≈7.82s
So, it would take approximately 7.82 seconds for the ball to hit the ground, ignoring air resistance.
Distance fallen after 3.0 seconds:
We can use the equation:
�
=
�
�
+
1
2
�
�
2
s=ut+
2
1
at
2
Where:
�
s is the displacement (which we want to find)
�
u is the initial velocity (0 m/s)
�
a is the acceleration due to gravity (approximately
9.81
m/s
2
9.81m/s
2
)
�
t is the time taken (3.0 seconds)
Substituting the given values:
�
=
0
×
3.0
+
1
2
×
9.81
×
(
3.0
)
2
s=0×3.0+
2
1
×9.81×(3.0)
2
�
=
0
+
1
2
×
9.81
×
9.0
s=0+
2
1
×9.81×9.0
�
=
0
+
1
2
×
88.29
s=0+
2
1
×88.29
�
=
0
+
44.145
s=0+44.145
�
=
44.145
m
s=44.145m
So, after 3.0 seconds, the ball has fallen approximately 44.145 meters.
Explanation:
