Question

A snail crawls at a pace of \(5.0 \mathrm{cm} / \mathrm{min.}\) Express the snail's speed in (a) \(\mathrm{ft} / \mathrm{s}\) and (b) $\mathrm{mi} / \mathrm{h}$.

Short answer

Question: A snail moves at a speed of 5.0 cm/min. Convert its speed to feet per second (ft/s) and miles per hour (mi/h). Answer: The snail's speed is approximately 0.3281 ft/s and 0.00186 mi/h.

Step-by-step solution

Identify conversion factors

First, let's gather the conversion factors required for this exercise: 1. To convert centimeters to feet: 1 ft = 30.48 cm 2. To convert centimeters to miles: 1 mi = 160934.4 cm 3. To convert minutes to seconds: 1 min = 60 s 4. To convert minutes to hours: 1 min = 1/60 h

Convert the speed from cm/min to ft/s

First, we will convert the speed from centimeters per minute to feet per second. Given speed: 5.0 cm/min Now, we will multiply the given speed by the conversion factors to get the speed in ft/s: $$\frac{5.0 \,\mathrm{cm}}{\mathrm{min}} \times \frac{1 \,\mathrm{ft}}{30.48 \,\mathrm{cm}} \times \frac{60 \,\mathrm{s}}{1 \,\mathrm{min}} = \frac{5.0 \times 1 \times 60}{30.48 \times 1} \,\mathrm{ft/s}$$ Calculate the value of speed in ft/s: $$\frac{5.0 \times 1 \times 60}{30.48 \times 1} = 0.3281 \,\mathrm{ft/s}$$ Thus, the speed of the snail in ft/s is approximately 0.3281 ft/s.

Convert the speed from cm/min to mi/h

Now, we will convert the speed from centimeters per minute to miles per hour. Given speed: 5.0 cm/min We will multiply the given speed by the conversion factors to get the speed in mi/h: $$\frac{5.0 \,\mathrm{cm}}{\mathrm{min}} \times \frac{1 \,\mathrm{mi}}{160934.4 \,\mathrm{cm}} \times \frac{60 \,\mathrm{min}}{1 \,\mathrm{h}} = \frac{5.0 \times 1 \times 60}{1 \times 160934.4} \,\mathrm{mi/h}$$ Calculate the value of speed in mi/h: $$\frac{5.0 \times 1 \times 60}{1 \times 160934.4} = 0.00186 \,\mathrm{mi/h}$$ Thus, the speed of the snail in mi/h is approximately 0.00186 mi/h. To summarize: a) The speed of the snail in ft/s is approximately 0.3281 ft/s. b) The speed of the snail in mi/h is approximately 0.00186 mi/h.