To determine which falling object will have the least kinetic energy upon collision with the ground, we can use the kinetic energy formula:
\[ KE = \frac{1}{2}mv^2 \]
where \( m \) is the mass of the object in kilograms and \( v \) is the velocity in meters per second.
Let's calculate the kinetic energy for each option:
-
10 grams of water falling at 1 m/s:
\[ m = 10 \text{ grams} = 0.01 \text{ kg}, \quad v = 1 \text{ m/s} \] \[ KE = \frac{1}{2} \times 0.01 \times (1)^2 = 0.005 \text{ J} \] -
100 grams of dirt falling at 15 m/s:
\[ m = 100 \text{ grams} = 0.1 \text{ kg}, \quad v = 15 \text{ m/s} \] \[ KE = \frac{1}{2} \times 0.1 \times (15)^2 = 11.25 \text{ J} \] -
10 grams of dirt falling at 2 m/s:
\[ m = 10 \text{ grams} = 0.01 \text{ kg}, \quad v = 2 \text{ m/s} \] \[ KE = \frac{1}{2} \times 0.01 \times (2)^2 = 0.02 \text{ J} \] -
100 grams of water falling at 10 m/s:
\[ m = 100 \text{ grams} = 0.1 \text{ kg}, \quad v = 10 \text{ m/s} \] \[ KE = \frac{1}{2} \times 0.1 \times (10)^2 = 5 \text{ J} \]
Now, let's summarize the kinetic energies calculated:
- 10 grams of water falling at 1 m/s: 0.005 J
- 100 grams of dirt falling at 15 m/s: 11.25 J
- 10 grams of dirt falling at 2 m/s: 0.02 J
- 100 grams of water falling at 10 m/s: 5 J
Comparing these values, the falling object that results in the least kinetic energy when it collides with the ground is:
10 grams of water falling at 1 m/s (0.005 J).
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