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:
\[ KE = \frac{1}{2}mv^2 \]
where \( KE \) is the kinetic energy, \( m \) is the mass of the object, and \( v \) is its velocity just before impact.
Now, let's calculate the kinetic energy for each option:
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100 grams of dirt falling at 15 m/s:
- Mass, \( m = 0.1 , kg \)
- Velocity, \( v = 15 , m/s \) \[ KE = \frac{1}{2} \times 0.1 \times 15^2 = \frac{1}{2} \times 0.1 \times 225 = 11.25 , J \]
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10 grams of dirt falling at 2 m/s:
- Mass, \( m = 0.01 , kg \)
- Velocity, \( v = 2 , m/s \) \[ KE = \frac{1}{2} \times 0.01 \times 2^2 = \frac{1}{2} \times 0.01 \times 4 = 0.02 , J \]
-
100 grams of water falling at 10 m/s:
- Mass, \( m = 0.1 , kg \)
- Velocity, \( v = 10 , m/s \) \[ KE = \frac{1}{2} \times 0.1 \times 10^2 = \frac{1}{2} \times 0.1 \times 100 = 5.0 , J \]
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10 grams of water falling at 1 m/s:
- Mass, \( m = 0.01 , kg \)
- Velocity, \( v = 1 , m/s \) \[ KE = \frac{1}{2} \times 0.01 \times 1^2 = \frac{1}{2} \times 0.01 \times 1 = 0.005 , J \]
Now we can compare the kinetic energies calculated:
- 100 grams of dirt at 15 m/s: 11.25 J
- 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
Among these, the object with the least kinetic energy when it collides with the ground is:
10 grams of water falling at 1 m/s (0.005 J).
1 answer