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 and \(v\) is its velocity.
Let's calculate the kinetic energy for each of the options given:
-
100 grams of water falling at 10 m/s:
- Mass = 100 grams = 0.1 kg
- Velocity = 10 m/s
- \[ KE = \frac{1}{2} \times 0.1 \times (10)^2 = \frac{1}{2} \times 0.1 \times 100 = 5 , \text{J} \]
-
10 grams of water falling at 1 m/s:
- Mass = 10 grams = 0.01 kg
- Velocity = 1 m/s
- \[ KE = \frac{1}{2} \times 0.01 \times (1)^2 = \frac{1}{2} \times 0.01 \times 1 = 0.005 , \text{J} \]
-
100 grams of dirt falling at 15 m/s:
- Mass = 100 grams = 0.1 kg
- Velocity = 15 m/s
- \[ KE = \frac{1}{2} \times 0.1 \times (15)^2 = \frac{1}{2} \times 0.1 \times 225 = 11.25 , \text{J} \]
-
10 grams of dirt falling at 2 m/s:
- Mass = 10 grams = 0.01 kg
- Velocity = 2 m/s
- \[ KE = \frac{1}{2} \times 0.01 \times (2)^2 = \frac{1}{2} \times 0.01 \times 4 = 0.02 , \text{J} \]
Now comparing the kinetic energies calculated:
- 100 grams of water at 10 m/s = 5 J
- 10 grams of water at 1 m/s = 0.005 J
- 100 grams of dirt at 15 m/s = 11.25 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.
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