The height of a rocket a given number of seconds after it is released is modeled by . What does t represent?

1 answer:

6 0

$\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \\\\ ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases}$

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amm1812

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3 years ago

What are the values of a and b?

ivann1987 [24]

Answer:

Step-by-step explanation:

Small triangles are similar. Therefore, the sides are proportional

$\dfrac{a}{20}=\dfrac{20}{21}$ <em>cross multiply</em>

$21a=(20)(20)$ <em>divide both sides by 21</em>

$a=\dfrac{400}{21}$

For b, we can use the Pythagorean theorem:

$b^2=\left(\dfrac{400}{21}\right)^2+20^2\\\\b^2=\dfrac{160000}{441}+400\\\\b^2=\dfrac{160000}{441}+\dfrac{176400}{441}\\\\b^2=\dfrac{336400}{441}\to b=\sqrt{\dfrac{336400}{441}}\\\\b=\dfrac{\sqrt{336400}}{\sqrt{441}}\\\\b=\dfrac{580}{21}$