Question

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 512 kilograms. How much kinetic energy do they have?

KE=12mv2


(1 point)
Responses

4,812.8 J
4,812.8 J

180.961.3 J
180.961.3 J

451,584.0 J
451,584.0 J

90,480.6 J

Answer 1

To calculate the kinetic energy (KE) of the racehorse and its jockey, we can use the formula:

\[
KE = \frac{1}{2} mv^2
\]

where:
- \( m \) is the mass (in kilograms),
- \( v \) is the velocity (in meters per second).

Given:
- \( m = 512 \) kg,
- \( v = 18.8 \) m/s.

Now, we can plug in the values:

\[
KE = \frac{1}{2} \times 512 \, \text{kg} \times (18.8 \, \text{m/s})^2
\]

First, calculate \( (18.8)^2 \):

\[
(18.8)^2 = 353.44 \, \text{m}^2/\text{s}^2
\]

Now substitute this back into the kinetic energy formula:

\[
KE = \frac{1}{2} \times 512 \times 353.44
\]

\[
KE = 256 \times 353.44
\]

\[
KE = 90581.44 \, \text{J}
\]

So the kinetic energy is approximately **90,581.44 joules**.

However, this value does not directly match any of the options. It seems we need to round it based on the provided options. Based on rounding:

- **90,480.6 J** seems to be the closest answer provided.

Therefore, the correct response is:

**90,480.6 J**