vertical motion

[jaclyncool7]

a stone is thrown veritcally has height = 160t-16t^2+14 feet t second after it is thrown. what is the maximum height the stone achieves?

 

[galactus]

The max height is the vertex of the parabola $\displaystyle h=at^{2}+bt+c$

The max height can be found by using $\displaystyle h=c-\frac{b^{2}}{4a}$


Oops, fixed typos

 

[BigGlenntheHeavy]

$\displaystyle S(t) \ = \ -16t^2+160t+14, \ distance \ formula.$

$\displaystyle V(t) \ = \ -32t \ +160, \ velocity \ formula, \ now \ when \ the \ velocity \ = \ 0, \ it \ has \ taken \ 5 \ seconds.$

$\displaystyle Hence, \ S(5) \ = \ 414 \ ft., \ the \ maximum \ height \ f(t) \ can \ achieve.$

$\displaystyle See \ graph.$

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