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.

Speed and height over time

Time (s) Speed (m/s) Height (m)
0.0 0 60
0.5 7 53
0.1 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

Answer 1

To determine when the ball has the highest kinetic energy, we need to consider that kinetic energy (KE) is given by the formula:

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

Where:
- \(m\) is the mass of the ball (which is constant and does not change the comparison),
- \(v\) is the speed of the ball at that time.

From the table, we can see the speed of the ball at different times:

- At 0.0 seconds, speed = 0 m/s
- At 0.5 seconds, speed = 7 m/s
- At 1.0 seconds, speed = 10 m/s
- At 1.5 seconds, speed = 15 m/s
- At 2.0 seconds, speed = 20 m/s
- At 2.5 seconds, speed = 0 m/s (the ball has hit the ground)

Since the mass is constant, we can focus on the square of the speed, \(v^2\), to analyze kinetic energy:

- At 0.0 seconds, \(v^2 = 0^2 = 0\)
- At 0.5 seconds, \(v^2 = 7^2 = 49\)
- At 1.0 seconds, \(v^2 = 10^2 = 100\)
- At 1.5 seconds, \(v^2 = 15^2 = 225\)
- At 2.0 seconds, \(v^2 = 20^2 = 400\)
- At 2.5 seconds, \(v^2 = 0^2 = 0\)

The highest speed occurs at 2.0 seconds when the speed is 20 m/s, which gives the highest kinetic energy.

Therefore, the point in time when the ball has the highest kinetic energy is:

**After 2 seconds**.