Question
A racehorse is running at 42 miles per hour, equivalent to 18.8 meters per second. The horse and its jockey have a combined mass of 520 kilograms. How much kinetic energy do they have?
KE = 1/2mv^2
(1 point)
451,584.0 J
90,480.6 J
91,894.4 J
458,640 J
KE = 1/2mv^2
(1 point)
451,584.0 J
90,480.6 J
91,894.4 J
458,640 J
Answers
GPT-4o mini
To calculate the kinetic energy (KE) of the racehorse and its jockey, we will use the kinetic energy formula:
\[
KE = \frac{1}{2} mv^2
\]
where:
- \( m \) is the mass in kilograms
- \( v \) is the velocity in meters per second
Given:
- \( m = 520 \) kg
- \( v = 18.8 \) m/s
Now substituting the values into the formula:
\[
KE = \frac{1}{2} \times 520 \, \text{kg} \times (18.8 \, \text{m/s})^2
\]
\[
KE = \frac{1}{2} \times 520 \times 353.44 \, \text{m}^2/\text{s}^2 \, \, (\text{since } 18.8^2 = 353.44)
\]
\[
KE = 260 \times 353.44
\]
\[
KE = 91,894.4 \, \text{J}
\]
Thus, the kinetic energy of the horse and its jockey is \( \text{91,894.4 J} \).
The correct answer is: **91,894.4 J**.
\[
KE = \frac{1}{2} mv^2
\]
where:
- \( m \) is the mass in kilograms
- \( v \) is the velocity in meters per second
Given:
- \( m = 520 \) kg
- \( v = 18.8 \) m/s
Now substituting the values into the formula:
\[
KE = \frac{1}{2} \times 520 \, \text{kg} \times (18.8 \, \text{m/s})^2
\]
\[
KE = \frac{1}{2} \times 520 \times 353.44 \, \text{m}^2/\text{s}^2 \, \, (\text{since } 18.8^2 = 353.44)
\]
\[
KE = 260 \times 353.44
\]
\[
KE = 91,894.4 \, \text{J}
\]
Thus, the kinetic energy of the horse and its jockey is \( \text{91,894.4 J} \).
The correct answer is: **91,894.4 J**.