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

10 grams of dirt falling at 2 m/s

Answer 1

To determine which falling object will have 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 in kilograms and \(v\) is the velocity in meters per second.

Let's calculate the kinetic energy for each object:

1. **100 grams of dirt falling at 15 m/s**:
- Mass \(m\) = 100 grams = 0.1 kg
- Velocity \(v\) = 15 m/s
\[
KE = \frac{1}{2}(0.1)(15^2) = 0.05 \cdot 225 = 11.25 \, \text{J}
\]

2. **100 grams of water falling at 10 m/s**:
- Mass \(m\) = 100 grams = 0.1 kg
- Velocity \(v\) = 10 m/s
\[
KE = \frac{1}{2}(0.1)(10^2) = 0.05 \cdot 100 = 5 \, \text{J}
\]

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

4. **10 grams of dirt falling at 2 m/s**:
- Mass \(m\) = 10 grams = 0.01 kg
- Velocity \(v\) = 2 m/s
\[
KE = \frac{1}{2}(0.01)(2^2) = 0.005 \cdot 4 = 0.02 \, \text{J}
\]

Now, let's summarize the kinetic energies calculated:

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

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