Dimensional Analysis is a powerful tool for anyone working with formulas and different units of measure. Sadly, our students might never experience the power and beauty of this strategy given the multitude of online resources that are ready and waiting to do the work for them.
Take advantage of your students’ interest in sports and competitions to motivate some investigations with dimensional analysis. One question you might pose is where do you think humans can achieve the greatest speed – on land or in water? Students can either collect their own data – if they have access to a swimming pool or other body of water – or find statistics of some of the world’s fastest runners and swimmers. For example, in the 2012 Summer Olympics, David Rudisha of Kenya broke the record for the men’s 800 meter race with a time of 1:40.91. In the same games, China’s Sun Yang broke the record for men’s 1500 meter freestyle with a time of 14:31.02. Since the swimmer swam almost twice as far as the runner ran, but took almost 9 times as long to get that far, it seems that humans are speedier on land.
But how do we compare to speedy animals that live on the land and in the water? The fastest animal on land is the cheetah, which can achieve maximum speeds of 75 miles per hour. In the ocean, the sailfish has been recorded at speeds of up to 70 miles per hour.
Let’s compare Rudisha’s record breaking run to the cheetah. We will use dimensional analysis to convert and cancel units so that the desired units remain.
First convert the seconds to minutes: 40.91 seconds x (1 minute/60 seconds) = .682 minute
(800 meters/1.682 minute) x (1 km/1,000 meters) x (0.62 miles/1 km) x (60 minutes/1 hour) = 17.7 miles per hour
Next compare Yang’s swim with the sailfish.
Again, converting the seconds to minutes, 31.02 seconds x (1 minute/60 seconds) = .517 minute
(1500 meters/14.517 minutes) x (1 km/1,000 meters) x (.62 miles/1 km) x (60 minutes/1 hour) = 3.84 miles per hour.
So while we humans are much faster on land than in water, even our Olympians are no match for the fastest creatures in each!