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3 years ago

12

Andrew measured the time it took for an apple to fall 50 feet as 1.95 seconds, but his calculations show that it should be 1.77

seconds. What was his experimental error?
SHOW YOUR WORK PLZ

1 answer:

Olin [163]3 years ago

6 0

Answer about 1.77 seconds.

f(t) = -16 t^2 + 25t + 6

f(t) = height.

hieght = 0 = -16t^2 + 25t + 6

Find t using the quadratic formula,

t = ( - 25 +/- √[25^2 - 4 (-16)(6)] ) / [2*(-16)]

t = [-25 +/- √ (625 + 384) ] / -32

t = [-25 +/- 31.76] / -32.

You will obtain two results one positive and one negative. Take the positive only as the other one has no physical meaning. t = 1.77 s.

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$\displaystyle f(x)=x^2+2x+2$

Step-by-step explanation:

<u>System Of Linear Equations </u>

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

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We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

$\displaystyle f(-1)=a(-1)^2+b(-1)+c$

$\displaystyle f(-1)=a-b+c$

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Now we use the second condition f(1)=5

$\displaystyle f(1)=a(1)^2+b(1)+c$

$\displaystyle f(1)=a+b+c$

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Finally, we use the third condition f(2)=10

$\displaystyle f(2)=a(2)^2+b(2)+c$

$\displaystyle f(2)=4a+2b+c$

$\displaystyle 4a+2b+c=10....[eq\ 3]$

We put together eq 1, eq 2, and eq 3 to form the system

$\displaystyle \left\{\begin{matrix}a-b+c=1\\ a+b+c=5\\ 4a+2b+c=10\end{matrix}\right.$

Adding the first two equations we have

$\displaystyle 2a+2c=6$

$\displaystyle a+c=3$

And also

$\displaystyle b=2$

Using the above equation and the value of b in the third equation, we have

$\displaystyle \left\{\begin{matrix}a+c=3\\ 4a+c=6\end{matrix}\right.$

Subtracting the first equation from the second

$\displaystyle 3a=3$

$\displaystyle a=1$

And therefore

$\displaystyle c=2$

Now we have all the values, the quadratic function is

$\displaystyle \boxed{f(x)=x^2+2x+2}$

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