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May the Force be with You!

October27

As a growing mathematician you will need to get really good at working with formulae. That is, you need to learn how to solve simple equations and use this knowledge to work with formulae. Another way of letting you in to this gently is that it is like you need to know the road rules before you start driving on them! Of course, there are different rules for different situations but general rules apply all the time. I was curious this morning when I saw the following picture on the web:

“What is this?” you might ask. It is a Ford Focus – a vehicle which carries a 5 star ANCAP safety rating. However, this car was travelling way faster than the speed it did for its safety rating. What does this mean? Well, you have to look at the formula for force:

“There is one totally important formula when it comes to forces, F = ma. That’s all there is, but everything revolves around that formula. “F” is the total (net) force, “m” is the object’s mass, and “a” is the acceleration that occurs. As a sentence, “The net force applied to the object equals the mass of the object multiplied by the amount of its acceleration.” More information about Force and other Physics formulae can be found at physics4kids.

May the Force be with you, but only if your acceleration is kept under control! Note: the Ford Focus is a very safe vehicle but only when the force of impact is calculated at quite low speed (64km/hr for frontal impact, ANCAP test), This image of the mangled Ford (no chance of survival) was the result of impact at 120 miles per hour. How fast is that in kms per hour? (hint: google for <weight and mass conversions>). Update: I had a reply from ANCAP which stated, “From real-world (USA) data, more than half of all fatalities to seat-belt wearing drivers in frontal crashes occur at impact speeds under 55km/h. ANCAP tried to address these fatalities, as well as considering higher impact speeds and 64km/h is considered a good balance.

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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