Question

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

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

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

10 grams of water falling at 1 m/s

Answer 1

To determine which falling object will result in the least kinetic energy when it collides 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 (in kilograms),
- \(v\) is the velocity of the object (in meters per second).

We will calculate the kinetic energy for each option:

1. **100 grams of dirt falling at 15 m/s:**
- Mass \(m = 100 \, \text{grams} = 0.1 \, \text{kg}\)
- Velocity \(v = 15 \, \text{m/s}\)
- \(KE = \frac{1}{2} \times 0.1 \times (15)^2 = 0.5 \times 0.1 \times 225 = 11.25 \, \text{J}\)

2. **100 grams of water falling at 10 m/s:**
- Mass \(m = 100 \, \text{grams} = 0.1 \, \text{kg}\)
- Velocity \(v = 10 \, \text{m/s}\)
- \(KE = \frac{1}{2} \times 0.1 \times (10)^2 = 0.5 \times 0.1 \times 100 = 5.0 \, \text{J}\)

3. **10 grams of dirt falling at 2 m/s:**
- Mass \(m = 10 \, \text{grams} = 0.01 \, \text{kg}\)
- Velocity \(v = 2 \, \text{m/s}\)
- \(KE = \frac{1}{2} \times 0.01 \times (2)^2 = 0.5 \times 0.01 \times 4 = 0.02 \, \text{J}\)

4. **10 grams of water falling at 1 m/s:**
- Mass \(m = 10 \, \text{grams} = 0.01 \, \text{kg}\)
- Velocity \(v = 1 \, \text{m/s}\)
- \(KE = \frac{1}{2} \times 0.01 \times (1)^2 = 0.5 \times 0.01 \times 1 = 0.005 \, \text{J}\)

Now we can compare the kinetic energies:

- **100 grams of dirt at 15 m/s:** 11.25 J
- **100 grams of water at 10 m/s:** 5.0 J
- **10 grams of dirt at 2 m/s:** 0.02 J
- **10 grams of water at 1 m/s:** 0.005 J

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