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A student drops a ball from a height of 60 meters. The table below shows the ball's speed and height as time passes.

Speed And Height Over Time
Time (s) | 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?
A. At the start (0 seconds)
B. After 0.5 seconds
C. After 2 seconds
D. After 2.5 seconds

3 answers

Kinetic energy (KE) is given by the formula:

\[ KE = \frac{1}{2} mv^2 \]

where \(m\) is the mass of the object and \(v\) is its speed. Since the mass of the ball remains constant, the kinetic energy is directly proportional to the square of the speed. Therefore, to determine when the ball has the highest kinetic energy, we need to find the point in time when the speed is at its maximum.

From the provided data:

  • At \(0.0\) s: Speed = \(0\) m/s
  • At \(0.5\) s: Speed = \(7\) m/s
  • At \(1.0\) s: Speed = \(10\) m/s
  • At \(1.5\) s: Speed = \(15\) m/s
  • At \(2.0\) s: Speed = \(20\) m/s
  • At \(2.5\) s: Speed = \(0\) m/s

The maximum speed occurs at \(2.0\) seconds, where the speed is \(20\) m/s. Therefore, the maximum kinetic energy occurs at this point in time.

Thus, none of the provided options directly include \(2.0\) seconds, but the point right before the speed starts to drop significantly (at \(2.0\) seconds) should be considered.

If we were to choose from the available options, option C. After 2 seconds would be the most relevant, as that is where the speed (and thus kinetic energy) is at its highest right before it starts to decrease.

So, the correct answer is C. After 2 seconds.

are you sure this is correct

Let's reevaluate the information to clarify the point at which the ball has the highest kinetic energy.

Kinetic energy (KE) is calculated using the formula:

\[ KE = \frac{1}{2} mv^2 \]

As stated, since mass \(m\) is constant, the kinetic energy depends only on the speed \(v\):

  • At \(0.0\) seconds: Speed = \(0\) m/s → KE = \(0\)
  • At \(0.5\) seconds: Speed = \(7\) m/s → KE = \(\frac{1}{2} m (7^2) = \frac{49}{2} m\)
  • At \(1.0\) seconds: Speed = \(10\) m/s → KE = \(\frac{1}{2} m (10^2) = 50 m\)
  • At \(1.5\) seconds: Speed = \(15\) m/s → KE = \(\frac{1}{2} m (15^2) = \frac{225}{2} m\)
  • At \(2.0\) seconds: Speed = \(20\) m/s → KE = \(200 m\)
  • At \(2.5\) seconds: Speed = \(0\) m/s → KE = \(0\)

The maximum speed, which corresponds to the maximum kinetic energy, occurs at \(2.0\) seconds with the speed of \(20\) m/s.

Despite this being the case, it's important to pick from the provided answer options, which were:

A. At the start (0 seconds)
B. After 0.5 seconds
C. After 2 seconds
D. After 2.5 seconds

Given that kinetic energy peaks at \(2.0\) seconds (which corresponds to the moment just before \(2.5\) seconds), option C. After 2 seconds correctly reflects the point at which the kinetic energy is maximized, since it references that moment.

So to confirm: C. After 2 seconds is indeed the correct answer. Thank you for your patience and for prompting a thorough reevaluation!