Kinetic energy (KE) can be calculated using the formula:
\[ \text{KE} = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the velocity of the object.
Let's calculate the kinetic energy for each case:
-
120 Kg of sand falling at 12 m/s \[ \text{KE} = \frac{1}{2} \times 120 , \text{kg} \times (12 , \text{m/s})^2 = \frac{1}{2} \times 120 \times 144 = 8640 , \text{J} \]
-
12 Kg of sand falling at 8 m/s \[ \text{KE} = \frac{1}{2} \times 12 , \text{kg} \times (8 , \text{m/s})^2 = \frac{1}{2} \times 12 \times 64 = 384 , \text{J} \]
-
12 Kg of water falling at 10 m/s \[ \text{KE} = \frac{1}{2} \times 12 , \text{kg} \times (10 , \text{m/s})^2 = \frac{1}{2} \times 12 \times 100 = 600 , \text{J} \]
-
120 Kg of water falling at 12 m/s \[ \text{KE} = \frac{1}{2} \times 120 , \text{kg} \times (12 , \text{m/s})^2 = \frac{1}{2} \times 120 \times 144 = 8640 , \text{J} \]
Comparing the kinetic energies:
- 120 Kg of sand at 12 m/s = 8640 J
- 12 Kg of sand at 8 m/s = 384 J
- 12 Kg of water at 10 m/s = 600 J
- 120 Kg of water at 12 m/s = 8640 J
The object with the least kinetic energy is 12 Kg of sand falling at 8 m/s, with a kinetic energy of 384 J.