Question
Calculate the kinetic energy of a 100.0-kg meteor approaching the Earth at a speed of 10.0 km/s. Remember that 1 km = 1000 m.
5.00 × 109 J
1.00 × 108 J
50.0 × 108 J
10 × 107 J
Answers
GPT-4o mini
The kinetic energy (KE) of an object can be calculated using the formula:
\[
KE = \frac{1}{2}mv^2
\]
where \( m \) is the mass of the object and \( v \) is its velocity.
Given:
- Mass of the meteor, \( m = 100.0 \, \text{kg} \)
- Speed of the meteor, \( v = 10.0 \, \text{km/s} = 10.0 \times 1000 \, \text{m/s} = 10000 \, \text{m/s} \)
Now, substituting the values into the kinetic energy formula:
\[
KE = \frac{1}{2} \times 100.0 \, \text{kg} \times (10000 \, \text{m/s})^2
\]
Calculating \( (10000 \, \text{m/s})^2 \):
\[
(10000 \, \text{m/s})^2 = 100000000000 \, \text{m}^2/\text{s}^2
\]
Now substituting back into the kinetic energy equation:
\[
KE = \frac{1}{2} \times 100.0 \times 100000000000 = 50.0 \times 1000000000 = 50.0 \times 10^9 \, \text{J}
\]
Thus, the kinetic energy of the meteor is:
\[
KE = 5.0 \times 10^9 \, \text{J}
\]
So, the correct answer is:
**5.00 × 10^9 J**
\[
KE = \frac{1}{2}mv^2
\]
where \( m \) is the mass of the object and \( v \) is its velocity.
Given:
- Mass of the meteor, \( m = 100.0 \, \text{kg} \)
- Speed of the meteor, \( v = 10.0 \, \text{km/s} = 10.0 \times 1000 \, \text{m/s} = 10000 \, \text{m/s} \)
Now, substituting the values into the kinetic energy formula:
\[
KE = \frac{1}{2} \times 100.0 \, \text{kg} \times (10000 \, \text{m/s})^2
\]
Calculating \( (10000 \, \text{m/s})^2 \):
\[
(10000 \, \text{m/s})^2 = 100000000000 \, \text{m}^2/\text{s}^2
\]
Now substituting back into the kinetic energy equation:
\[
KE = \frac{1}{2} \times 100.0 \times 100000000000 = 50.0 \times 1000000000 = 50.0 \times 10^9 \, \text{J}
\]
Thus, the kinetic energy of the meteor is:
\[
KE = 5.0 \times 10^9 \, \text{J}
\]
So, the correct answer is:
**5.00 × 10^9 J**