Question

Which falling object has the least kinetic energy when it collides on the ground?(1 point)
Responses

120 Kg of sand falling 12 m/s
120 Kg of sand falling 12 m/s

12 Kg of sand falling at 8 m/s
12 Kg of sand falling at 8 m/s

12 Kg of water falling at 10 m/s
12 Kg of water falling at 10 m/s

120 Kg of water falling at 12 m/s
120 Kg of water falling at 12 m/s

Answer 1

To determine which falling object has 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 and \(v\) is its velocity.

Let's calculate the kinetic energy for each of the given objects:

1. **120 Kg of sand falling at 12 m/s:**
\[
KE = \frac{1}{2} \times 120 \, kg \times (12 \, m/s)^2 = \frac{1}{2} \times 120 \times 144 = 8640 \, J
\]

2. **12 Kg of sand falling at 8 m/s:**
\[
KE = \frac{1}{2} \times 12 \, kg \times (8 \, m/s)^2 = \frac{1}{2} \times 12 \times 64 = 384 \, J
\]

3. **12 Kg of water falling at 10 m/s:**
\[
KE = \frac{1}{2} \times 12 \, kg \times (10 \, m/s)^2 = \frac{1}{2} \times 12 \times 100 = 600 \, J
\]

4. **120 Kg of water falling at 12 m/s:**
\[
KE = \frac{1}{2} \times 120 \, kg \times (12 \, m/s)^2 = \frac{1}{2} \times 120 \times 144 = 8640 \, J
\]

Now, we summarize the kinetic energies calculated:

- 120 Kg of sand falling at 12 m/s: **8640 J**
- 12 Kg of sand falling at 8 m/s: **384 J**
- 12 Kg of water falling at 10 m/s: **600 J**
- 120 Kg of water falling at 12 m/s: **8640 J**

From these calculations, we can see that the object with the least kinetic energy is **12 Kg of sand falling at 8 m/s**, with a kinetic energy of **384 J**.