Question

Jim Shorts and his friend, Brock Lee, are competing against each other in a 100 meter sprint. Jim said he ran the race in
`4^(2)` seconds, and Brock said he ran the race in
`4^(-2)` seconds. Who is lying? How do you know? Explain.

Answer 1

Brock is lying because
`4^(-2)` seconds is equal to
`1/4^2=1/16=0.0625` seconds which is way less than one second.

Step-by-step explanation:

You can tell that It is not possible that Brock ran the reace in
`4^(-2)` seconds for several reasons:

• none chronometer has the precision to measure tenthousandths seconds,

• the world record for 100 m sprint is greater than 9 seconds, an even the fastest animal, cannot run the 100 m in less than one second,

• when you calculate the speed (see below) of 100 m in 0.00625 seconds, it is faster than the speed that any object in the world can reach.

To have an idea of what runnning 100 meters in 0.0625 secons means, convert that speed to kilometers per hour:

• speed = distance / time

• speed = 100 m / 0.0625 s =

100 m × 1 km / 1000 m × 1/0.0625 s × 3600 s/h = 5,760,000 km/h

Clearly, 5,760,000 km/h is greater than the speed that any object (car, plane, . . .) can reach.