**OUTCOME A3: Demonstrate an understanding of the role of Irrational Numbers in applications**

**ORIGINATORS: **

Emily and Isaac.

**EXPLANATION: **

Although it would be nice and easy to be able to solve all equations with rational numbers, in real life, it isn’t always like that. If you threw a baseball into the air, you would have to predict exactly where it would land in order to ensure that it would land on a rational number, and that is humanly impossible. In order to get a precise answer; irrational numbers would have to be used.

**SAMPLE PROBLEM:**

One sunny day, Joe-Bob decided to jump off a 1001m building. When he was 1m away from the ground, he noticed a giant rabid mongoose nearby, and thought it would be a good idea to use his Jetpack to fly to safety. Miraculously, he both fell and flew at the same speed. During his fall, his altitude could be calculated by using the following quadratic relationship:

a = 1000 - 2.74t² when a represents altitude and t represents time in seconds.

a) How long did it take him to reach 36m above groundlevel?

b) How long did it take him to reach 1001m again?

*This situation isn't rational AT ALL.*

**SOLUTION:**

a) a = 1000 - 2.74t²

36 = 1000 - 2.74t²

-36 -36

0 = 964 - 2.74t²

-964 -964

__-964__ = __-2.74t²__

-2.74-2.74

√t² = √351.82481751824817518248175182482

*t **= ± *18.756993829455939104560278824991s

b) a = 1000 - 2.74t²

0= 1000 - 2.74t²

-1000 -1000

__-1000__ = __-2.74t²__

-2.74 -2.74

√t² = √364.963503649635036496350649635

t = ± 19.10401799752175266193239179043s

since Joe-Bob was travelling at a constant speed, we can multiply it by 2 to find out how long it took him to get back up to his original height.

*Time taken to get back to original height = *19.10401799752175266193239179043s (2)

38.208035995043505323864783580861s

## Comments (1)

## Anonymous said

at 8:22 pm on Mar 13, 2007

Emily and Isaac, I LOVE the giant rabid mongoose. Very creative. There are some problems with your sample problem however. The -t^2 means that the graph is a reflection but it's not supposed to be. Also your y-intercept isn't 1001 which it should be. Something like y=9.9x^2 -198x +1001 would be a much better equation.

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