Question

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

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

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

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

Answer 1

To determine which falling object will result in the least kinetic energy upon collision 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, and \( v \) is the velocity in meters per second.

Let's calculate the kinetic energy for each option:

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

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

3. **10 grams of water falling at 1 m/s:**
- Mass: \( m = 10 \, \text{grams} = 0.01 \, \text{kg} \)
- Velocity: \( v = 1 \, \text{m/s} \)
- \( KE = \frac{1}{2} \times 0.01 \times (1)^2 = \frac{1}{2} \times 0.01 \times 1 = 0.005 \, \text{J} \)

4. **100 grams of dirt falling at 15 m/s:**
- Mass: \( m = 100 \, \text{grams} = 0.1 \, \text{kg} \)
- Velocity: \( v = 15 \, \text{m/s} \)
- \( KE = \frac{1}{2} \times 0.1 \times (15)^2 = \frac{1}{2} \times 0.1 \times 225 = 11.25 \, \text{J} \)

Now, summarizing the kinetic energies:
- 10 grams of dirt at 2 m/s: **0.02 J**
- 100 grams of water at 10 m/s: **5.0 J**
- 10 grams of water at 1 m/s: **0.005 J**
- 100 grams of dirt at 15 m/s: **11.25 J**

Based on the calculations, the object that results in the least kinetic energy upon collision with the ground is **10 grams of water falling at 1 m/s (0.005 J)**.