Question

Which falling object will result in the least kinetic energy when it collides with the ground?(1 point)
Responses

100 grams of dirt falling at 15 m/s
100 grams of dirt falling at 15 m/s

10 grams of water falling at 1 m/s
10 grams of water falling at 1 m/s

10 grams of dirt falling at 2 m/s
10 grams of dirt falling at 2 m/s

100 grams of water falling at 10 m/s
100 grams of water falling at 10 m/s

Answer 1

To determine which object will have 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 the velocity.

Let's calculate the kinetic energy for each option:

1. **100 grams of dirt falling at 15 m/s:**
- Mass = 100 grams = 0.1 kg
- Velocity = 15 m/s
\[
KE = \frac{1}{2} \times 0.1 \times (15)^2 = \frac{1}{2} \times 0.1 \times 225 = 11.25 \, \text{J}
\]

2. **10 grams of water falling at 1 m/s:**
- Mass = 10 grams = 0.01 kg
- Velocity = 1 m/s
\[
KE = \frac{1}{2} \times 0.01 \times (1)^2 = \frac{1}{2} \times 0.01 \times 1 = 0.005 \, \text{J}
\]

3. **10 grams of dirt falling at 2 m/s:**
- Mass = 10 grams = 0.01 kg
- Velocity = 2 m/s
\[
KE = \frac{1}{2} \times 0.01 \times (2)^2 = \frac{1}{2} \times 0.01 \times 4 = 0.02 \, \text{J}
\]

4. **100 grams of water falling at 10 m/s:**
- Mass = 100 grams = 0.1 kg
- Velocity = 10 m/s
\[
KE = \frac{1}{2} \times 0.1 \times (10)^2 = \frac{1}{2} \times 0.1 \times 100 = 5 \, \text{J}
\]

Now, let's summarize the kinetic energy for each option:

- 100 grams of dirt at 15 m/s: 11.25 J
- 10 grams of water at 1 m/s: 0.005 J
- 10 grams of dirt at 2 m/s: 0.02 J
- 100 grams of water at 10 m/s: 5 J

The option with the least kinetic energy is **10 grams of water falling at 1 m/s** with **0.005 J** of kinetic energy.