Question

Which falling object will result in the
least
kinetic energy as it collides with the ground?
(1 point)
a ball with a mass of 10 grams falling at 1 m/s
a toy plane with a mass of 10 grams falling at 2 m/s
a ball with a mass of 100 grams falling at 10 m/s
a toy plane with a mass of 100 grams falling at 15 m/s

Answer 1

To find the object that will result in the least kinetic energy upon colliding with the ground, we can use the formula for kinetic energy (\(KE\)):

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

where \(m\) is the mass of the object and \(v\) is its velocity just before the collision.

Let's calculate the kinetic energy for each object:

1. **A ball with a mass of 10 grams (0.01 kg) falling at 1 m/s:**
\[
KE = \frac{1}{2} \times 0.01 \, \text{kg} \times (1 \, \text{m/s})^2 = \frac{1}{2} \times 0.01 \times 1 = 0.005 \, \text{J}
\]

2. **A toy plane with a mass of 10 grams (0.01 kg) falling at 2 m/s:**
\[
KE = \frac{1}{2} \times 0.01 \, \text{kg} \times (2 \, \text{m/s})^2 = \frac{1}{2} \times 0.01 \times 4 = 0.02 \, \text{J}
\]

3. **A ball with a mass of 100 grams (0.1 kg) falling at 10 m/s:**
\[
KE = \frac{1}{2} \times 0.1 \, \text{kg} \times (10 \, \text{m/s})^2 = \frac{1}{2} \times 0.1 \times 100 = 5 \, \text{J}
\]

4. **A toy plane with a mass of 100 grams (0.1 kg) falling at 15 m/s:**
\[
KE = \frac{1}{2} \times 0.1 \, \text{kg} \times (15 \, \text{m/s})^2 = \frac{1}{2} \times 0.1 \times 225 = 11.25 \, \text{J}
\]

Now, summarizing the kinetic energy results:
- A ball (10g, 1m/s): 0.005 J
- A toy plane (10g, 2m/s): 0.02 J
- A ball (100g, 10m/s): 5 J
- A toy plane (100g, 15m/s): 11.25 J

The object that will result in the least kinetic energy upon colliding with the ground is **the ball with a mass of 10 grams falling at 1 m/s**, which has a kinetic energy of **0.005 J**.