Question 1177358
a) Find the horizontal distance the ball travels until it first hits the ground. Show work.
Use both the factoring method and the quadratic formula method to obtain your answer.

{{{h= -0.25d^2 + 0.8d}}}

when a soccer ball hits the ground,{{{ h=0 }}}

{{{0= -0.25d^2 + 0.8d}}}......factor

{{{0= (-0.25d + 0.8)d}}}

-> {{{d=0}}}
{{{-0.25d + 0.8=0 }}}
 {{{0.8=0.25d }}}
{{{ d=0.8/0.25}}}
{{{d=3.2}}}


using the quadratic formula method:


{{{h= -0.25d^2 + 0.8d}}}  => {{{a=-0.25}}},{{{ b= 0.8}}}, {{{c=0}}} 


{{{d=(-0.8+-sqrt(0.8^2-4(-0.25)*0)))/(2(-0.25))}}}

{{{d=(-0.8+-sqrt(0.8^2))/(-0.50)}}}

{{{d=(-0.8+-0.8)/(-0.50)}}}

=>

{{{d=(-0.8+0.8)/(-0.50)=0/-0.50=0}}}

or

{{{d=(-0.8-0.8)/(-0.50)=-1.6/-0.50=3.2}}}->the horizontal distance the ball travels until it first hits the ground


in case you need these questions:

b) Find the horizontal distance when the ball reaches its maximum height. Make a sketch. Show work.

{{{h= -0.25d^2 + 0.8d}}} 

max is at {{{vertex}}}, 

{{{-b/2a=-0.8/(2(-0.25))=1.6}}}

the horizontal distance when the ball reaches its maximum height is {{{d=1.6}}}


c) Find the maximum height of the ball using the distance you just determined in part b.

{{{h= -0.25*1.6^2 + 0.8*1.6 }}}
{{{h= -0.25*1.6^2 + 0.8*1.6 }}}
{{{h= -0.64+ 1.28 }}}
{{{h= 0.64 }}}