100 Meter Dash To Mph

How Fast is Usain Bolt?

Alignments to Content Standards: 7.RP.A.3

Task

Jamaican sprinter Usain Bolt won the 100 meter sprint aureate medal in the 2012 Summer Olympics. He ran the 100 meter race in nine.63 seconds. There are about 3.28 feet in a meter and 5280 anxiety in a mile. What was Usain Bolt's boilerplate speed for the 100 meter race in miles per 60 minutes?

IM Commentary

This task involves a multi-stride conversion between two rates, going from meters per second to miles per hr. In this case, the units coming from the 100 meter race are meters per 2nd and we do not have a skillful intuition for what this means in miles per hour. Nigh of united states are used to thinking virtually speeds in terms of miles per hour since the speedometers in our automobiles use these units, and so information technology is good for students to be able to convert between miles per hour and other units for speed that naturally come up.

The showtime solution shows all units in the calculations and does not make any calculations until the end. The 2nd solution goes step by footstep and provides an excellent opportunity to talk over rounding error as it is important hither to brand all calculations (equally in the first method) earlier rounding rather than using the rounded numbers for successive calculations.

In addition to the piece of work on conversion of units, information technology might be interesting to compare the top speed of the fastest human existence to some familiar animals:

Animal	Meridian Speed (in mph)
Hippopotamus	19
Kangaroo	45
Equus caballus	47
Gazelle	50
Cheetah	70

Remarkably, of the animals in the tabular array, the fastest human beings can just run faster than the hippopotamus. Notation that the speed calculated in this problem is the boilerplate speed for 100 meters which is a piddling less than the tiptop speed, but 23mph is significantly less than any of the other animals on the listing. For a more creative implementation of this task, the teacher could provide the table of different animate being speeds and inquire the students how the fastest human being beings would off-white against them in a race.

The relevant practice standards for this problem are MP2, Reason abstractly and quantitatively, as students move betwixt the context and the calculations, and MP6, Attend to precision, as students must focus on units and the accuracy with which they nowadays their final answer. Note that both the fourth dimension for the 100 meter race and the conversion from meters to feet are given with iii digit, so only three digits should remain in the answer. Likewise, given the number of steps required to solve this problem, it is well aligned to MP1, Make sense of problems and persevere in solving them.

Given the complexity of the problem, it would non exist appropriate for high-stakes summative cess only would be very appropriate in an instructional setting.

Solutions

Solution: 1 Table

We can make a tabular array of distances and times and so discover the corresponding charge per unit at the finish. In this solution, each successive line in the table represents a unmarried unit of measurement conversion, either for distance or for time. The method used hither kickoff finds how many anxiety per 2d Usain Bolt is running and and so moves from here to miles per hour.

Usain Commodities traveled 100 meters in 9.63 seconds. 1 meter is three.28 anxiety, and so 100 meters is $100\times 3.28=328$ feet.
Usain Bolt traveled 328 feet in 9.63 seconds. This means he traveled 1 foot in $9.63 \div 328 = 0.02936$ seconds.
Usain Bolt traveled 1 foot in 0.02936 seconds. 1 mile is 5280 feet, so at this speed, he would travel 1 mile in $5280\times0.02936=155$ seconds.
At this speed, Usain Commodities would travel 1 mile in 155 seconds. i hour is $threescore\times60=3600$ seconds, so he traveled 1 mile in $155\div3600=0.043056$ hours.
At this speed, Usain Commodities would travel 1 mile in 0.043056 hours. This means he would travel $1\div 0.043056 \approx 23.ii$ miles in 1 hr.
At this speed, Usain Commodities would travel 23.2 miles in 1 hour.

Distance Travelled	Time
100 meters	nine.63 seconds
328 feet	ix.63 seconds
one human foot	0.29 seconds
ane mile	155 seconds
1 mile	0.043 hours
23.2 miles	ane hour

The last line in the tabular array tells shows that Usain Commodities is running a little over 23 miles per hour.

In this tabular array the measurements of ix.63 seconds and 100 meters are not exact. The other measurement, in these calculations, which is not verbal is the 3.28 feet per meters. In a state of affairs similar this, all further numbers need to be appropriately rounded. The rounding must come at the end, however, after making all calculations: for example, the 0.29 seconds to run a foot is a rounded number. So in the next footstep when this is used to find how long information technology would take Usain Bolt to run one mile, the adding needs to be done not with 0.29 seconds but with nine.63 $\div$ 328 seconds.

Solution: 2 Unit of measurement conversions

We are given that Usain Bolt ran 100 meters in 9.63 seconds. Nosotros first decide how many meters per second this is:

\begin{align} 100 \,\mbox{meters} \div 9.63 \,\mbox{seconds} &= \frac{100}{9.63} \,\frac{{\rm meters}}{{\rm second}} \end{align}

Next we apply the fact that there are virtually 3.28 meters per foot to convert the speed to anxiety per second:

\begin{align} 100 \,\mbox{meters} \div 9.63 \,\mbox{seconds} &= \frac{100}{9.63} \,\frac{{\rm meters}}{{\rm second}}\\ &=\frac{100}{9.63} \times 3.28 \,\frac{{\rm anxiety}}{{\rm meter}} \times \frac{{\rm meters}}{{\rm second}} \\ &= \frac{100 \times 3.28}{9.63} \,\frac{{\rm feet}}{{\rm second}}. \terminate{align}

Adjacent we convert feet to miles. There are 5280 anxiety in a mile then this gives:

\brainstorm{align} 100 \,\mbox{meters} \div 9.63 \,\mbox{seconds} &= \frac{100 \times 3.28}{9.63} \frac{{\rm mile}}{{\rm 5280 \, feet}} \times \frac{{\rm anxiety}}{{\rm second}} \\ &= \frac{100\times 3.28}{9.63 \times 5280} \frac{{\rm miles}}{{\rm second}}. \end{marshal}

Finally at that place are 60 seconds per minute and lx minutes per hour so this is $60 \times threescore = 3600$ seconds per hr. Using this nosotros can now convert our original data in terms of meters per second to miles per hour:

\brainstorm{align} 100 \,\mbox{meters} \div 9.63 \,\mbox{seconds} &= \frac{100\times 3.28}{9.63 \times 5280} \frac{{\rm miles}}{{\rm second}}\\ &= \frac{100 \times 3.28}{ix.63 \times 5280} \frac{{\rm 3600 \, seconds}}{{\rm hour}} \times \frac{{\rm miles}}{{\rm second}} \\ &= \frac{100 \times 3.28 \times 3600}{9.63 \times 5280} \frac{{\rm miles}}{{\rm 60 minutes}}. \end{align}

Using a calculator, we find that Usain Bolt's average speed over the 100 meter race was near 23.2 miles per 60 minutes. Notation that some of the numbers in this calculation, namely 100, 3600, and 5280 are exact while 3.28 and 9.63 are just estimate. Since the estimate numbers simply take 3 significant digits we only study three digits in the final answer.