Question

A sprinter can run at a top speed of 0.32 miles per minute. Express her speed in (a) \(\mathrm{m} / \mathrm{s}\) and (b) \(\mathrm{mi} / \mathrm{h}\).

Short answer

Answer: The sprinter's top speed in meters per second is 8.61 m/s and in miles per hour is 19.2 mi/h.

Step-by-step solution

Convert miles per minute to meters per second

To convert the speed from miles per minute to meters per second, we use the conversion rates given above: 1. Multiply the given speed by the conversion rate from miles to meters. 2. Divide the result by the conversion rate from minutes to seconds. So, the equation will be: Speed\((\frac{m}{s})\) = Speed\((\frac{mi}{min}) \times \frac{1609.34 m}{1 mi} \times \frac{1 min}{60 s}\) Plug in the given speed (0.32 miles per minute): Speed\((\frac{m}{s}) = 0.32 \frac{mi}{min} \times \frac{1609.34 m}{1 mi} \times \frac{1 min}{60 s} = 8.61 \frac{m}{s}\)

Convert miles per minute to miles per hour

To convert the speed from miles per minute to miles per hour, we use the conversion rate between minutes and hours: Speed\((\frac{mi}{h})\) = Speed\((\frac{mi}{min}) \times \frac{60 min}{1 h}\) Plug in the given speed (0.32 miles per minute): Speed\((\frac{mi}{h}) = 0.32 \frac{mi}{min} \times \frac{60 min}{1 h} = 19.2 \frac{mi}{h}\) The sprinter's top speed in meters per second is 8.61 m/s and in miles per hour is 19.2 mi/h.