Question
A student drops a ball from a height of 60 meters. The table below shows the ball’s speed and height as time passes.
Times Speed (m/s) Height (m)
0.0 0 60
0.5 7 53
1.0 10 43
1.5 15 28
2.0 20 8
2.5 0 0
At what point in time does the ball have the highest kinetic energy?
(1 point)
Responses
At the start (0 seconds)
At the start (0 seconds)
After 0.5 seconds
After 0.5 seconds
After 2 seconds
After 2 seconds
After 2.5 seconds
After 2.5 seconds
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Times Speed (m/s) Height (m)
0.0 0 60
0.5 7 53
1.0 10 43
1.5 15 28
2.0 20 8
2.5 0 0
At what point in time does the ball have the highest kinetic energy?
(1 point)
Responses
At the start (0 seconds)
At the start (0 seconds)
After 0.5 seconds
After 0.5 seconds
After 2 seconds
After 2 seconds
After 2.5 seconds
After 2.5 seconds
Skip to navigation
Answers
GPT-4o mini
To determine the point in time when the ball has the highest kinetic energy, we need to understand that kinetic energy (KE) is given by the formula:
\[
KE = \frac{1}{2} mv^2
\]
where \( m \) is the mass of the object (in this case, the ball), and \( v \) is its speed.
Since we don't have the mass of the ball, we can compare the kinetic energies relative to each time point by focusing on the speed, because \( m \) is a constant factor. The higher the speed, the higher the kinetic energy, all other factors being equal.
Looking at the table, we can see the speeds at each time:
- At 0.0 seconds: Speed = 0 m/s (KE = 0)
- After 0.5 seconds: Speed = 7 m/s
- After 1.0 seconds: Speed = 10 m/s
- After 1.5 seconds: Speed = 15 m/s
- After 2.0 seconds: Speed = 20 m/s
- After 2.5 seconds: Speed = 0 m/s (the ball is on the ground)
The highest speed occurs at 2.0 seconds when the speed is 20 m/s. Therefore, the ball has the highest kinetic energy at:
**After 2 seconds**.
\[
KE = \frac{1}{2} mv^2
\]
where \( m \) is the mass of the object (in this case, the ball), and \( v \) is its speed.
Since we don't have the mass of the ball, we can compare the kinetic energies relative to each time point by focusing on the speed, because \( m \) is a constant factor. The higher the speed, the higher the kinetic energy, all other factors being equal.
Looking at the table, we can see the speeds at each time:
- At 0.0 seconds: Speed = 0 m/s (KE = 0)
- After 0.5 seconds: Speed = 7 m/s
- After 1.0 seconds: Speed = 10 m/s
- After 1.5 seconds: Speed = 15 m/s
- After 2.0 seconds: Speed = 20 m/s
- After 2.5 seconds: Speed = 0 m/s (the ball is on the ground)
The highest speed occurs at 2.0 seconds when the speed is 20 m/s. Therefore, the ball has the highest kinetic energy at:
**After 2 seconds**.