Question

The approximate maximum speeds of various animals follow, but in different units of speed. Convert these data to \(\mathrm{m} / \mathrm{s}\), and thereby arrange the animals in order of increasing maximum speed: squirrel, \(19 \mathrm{~km} / \mathrm{h}\); rabbit, 30 knots; snail, \(0.030 \mathrm{mi} / \mathrm{h}\); spider, \(1.8 \mathrm{ft} / \mathrm{s}\); cheetah, \(1.9 \mathrm{~km} / \mathrm{min}\); human, \(1000 \mathrm{~cm} / \mathrm{s} ;\) fox, \(1100 \mathrm{~m} / \mathrm{min} ;\) lion, \(1900 \mathrm{~km} /\) day.

Short answer

After converting all the given speeds to \( \mathrm{m} / \mathrm{s} \) and arranging them in increasing order, the result is: Snail (0.0134 \( \mathrm{m} / \mathrm{s} \)), Spider (0.55 \( \mathrm{m} / \mathrm{s} \)), Squirrel (5.28 \( \mathrm{m} / \mathrm{s} \)), Human (10 \( \mathrm{m} / \mathrm{s} \)), Rabbit (15.42 \( \mathrm{m} / \mathrm{s} \)), Fox (18.33 \( \mathrm{m} / \mathrm{s} \)), Lion (22.01 \( \mathrm{m} / \mathrm{s} \))

Step-by-step solution

Calculate Squirrel's Speed

First, let's convert squirrel's speed from \(\mathrm{km} / \mathrm{h}\) to \(\mathrm{m} / \mathrm{s}\). The conversion factor between these units is \( \frac{1 \mathrm{km}}{1000 \mathrm{m}} \) and \( \frac{1 \mathrm{h}}{3600 \mathrm{s}} \). Hence, the speed of squirrel is \( \frac{19 \mathrm{km} / \mathrm{h}}{1} \cdot \frac{1000 \mathrm{m}}{1 \mathrm{km}} \cdot \frac{1 \mathrm{h}}{3600 \mathrm{s}} = 5.28 \mathrm{m} / \mathrm{s} \)

Calculate Rabbit's Speed

Secondly, the rabbit's speed needs to be converted from knots to \( \mathrm{m} / \mathrm{s} \). One knot equals \(0.514 \mathrm{m} / \mathrm{s}\). So, the speed of a rabbit is \(30 \mathrm{knots} \cdot 0.514 \mathrm{m} / \mathrm{s} = 15.42 \mathrm{m} / \mathrm{s} \)

Calculate Snail's Speed

Thirdly, convert the snail's speed from \(\mathrm{mi} / \mathrm{h}\) to \(\mathrm{m} / \mathrm{s}\). One \(\mathrm{mi} / \mathrm{h}\) is approximately \(0.447 \mathrm{m} / \mathrm{s}\). Therefore, the snail's speed is \(0.03 \mathrm{mi} / \mathrm{h} \cdot 0.447 \mathrm{m} / \mathrm{s} = 0.0134 \mathrm{m} / \mathrm{s} \)

Calculate Spider's Speed

4th, convert spider's speed from \(\mathrm{ft} / \mathrm{s}\) to \(\mathrm{m} / \mathrm{s}\). The conversion factor is \( \frac{1 \mathrm{ft}}{0.305 \mathrm{m}} \), therefore, the speed of spider is \(1.8 \mathrm{ft} / \mathrm{s} \cdot \frac{0.305 \mathrm{m}}{1 \mathrm{ft}} = 0.55 \mathrm{m} / \mathrm{s}\)

Calculate Human's Speed

The 5th step consists of converting the human speed from \(\mathrm{cm} / \mathrm{s}\) to \(\mathrm{m} / \mathrm{s}\). In this case, it's needed to divide by 100, hence the human speed is \( \frac{1000 \mathrm{cm} / \mathrm{s}}{100} = 10 \mathrm{m} / \mathrm{s} \)

Calculate Fox's Speed

Using the conversion factor \( \frac{1 \mathrm{min}}{60 \mathrm{s}} \), the fox speed is \( \frac{1100 \mathrm{m} / \mathrm{min}}{1} \cdot \frac{1 \mathrm{min}}{60 \mathrm{s}} = 18.33 \mathrm{m} / \mathrm{s} \)

Calculate Lion's Speed

Finally, to find out lion's speed, you should use the conversion factors \( \frac{1 \mathrm{km}}{1000 \mathrm{m}} \), \( \frac{1 \mathrm{day}}{24 \mathrm{h}} \) and \( \frac{1 \mathrm{h}}{3600 \mathrm{s}} \), hence the lion's speed is \( \frac{1900 \mathrm{km} / \mathrm{day}}{1} \cdot \frac{1000 \mathrm{m}}{1 \mathrm{km}} \cdot \frac{1 \mathrm{day}}{24 \mathrm{h}} \cdot \frac{1 \mathrm{h}}{3600 \mathrm{s}} = 22.01 \mathrm{m} / \mathrm{s} \)

Key concepts

Speed Calculation

Calculating speed involves knowing the distance traveled over a certain period. The formula to find speed is simple: speed equals distance divided by time. To calculate speed accurately, ensure both distance and time are in consistent units.

For example, consider the squirrel that moves at 19 km/h. Since we want the result in meters per second, we convert kilometers to meters (1 km = 1000 m), and hours to seconds (1 hour = 3600 seconds). Using the formula:

• Convert kilometers to meters: \(19\,\text{km/h} \times \frac{1000\,\text{m}}{1\,\text{km}} = 19000\,\text{m/h}\).
• Convert hours to seconds: \(19000\,\text{m/h} \times \frac{1\,\text{h}}{3600\,\text{s}} = 5.28\,\text{m/s}\).

It’s crucial to get these unit conversions right to ensure the calculated speed is meaningful and correct.

Meters per Second

Meters per second (m/s) is the standard international unit for measuring speed, which indicates how many meters an object travels in one second. It is universally used for scientific calculations because it's part of the metric system.

When converting to meters per second, it involves changing the original unit of distance and the unit of time into meters and seconds, respectively. This ensures uniformity and ease in comparing speeds.

For instance, if a rabbit has a speed measured in knots, one might initially struggle without knowing that one knot equals approximately 0.514 meters per second. Thus, converting rabbit's 30 knots into m/s would mean multiplying by 0.514, resulting in 15.42 m/s.

Such conversions are crucial in contexts like comparing different animals, as found in the exercise, ensuring all speeds measure up equivalently.

Animal Speeds

Animals in the wild move at diverse speeds, and these speeds can be measured in a variety of units based on regional practices and the context of measurement.

With an exercise focusing on animals like squirrels, rabbits, and cheetahs, understanding general nature behaviors can be fascinating. Notice how a snail, at 0.030 miles per hour, is relatively slower than the blazing speed of a cheetah at 1.9 km/minute, which converts to 31.67 m/s.

Such conversions allow for comparison to determine which animals are the fastest accurately and efficiently.

• The lion, for example, speeds at 22.01 m/s.
• A rabbit, although swift in its regard, caps at 15.42 m/s once converted.

Exploring these numbers can provide insights into the physical capabilities and real-world contexts of these animals.