Question 680405
{{{s(t)=-16t^2+208t}}}



(a) make a sketch of what is happening




{{{drawing(600, 600, -10,20, -350, 800,grid(1),circle(3.7,550,0.2),circle(9.3,550,0.2),circle(13,0,0.3),graph(600, 600, -10,20, -350, 800,-16x^2+208x))}}}

(b) When will the rocket be 550 feet from the ground

{{{550ft=-16t^2+208t}}}

{{{0=-16t^2+208t-550ft}}}


{{{t = (-208 +- sqrt( 208^2-4*(-16)*(-550) ))/(2*(-16)) }}}


{{{t = (-208 +- sqrt( 43264-35200 ))/-32) }}}


{{{t = (-208 +- sqrt( 8064 ))/-32) }}}


{{{t = (-208 +- 89.8)/-32) }}}

solution:

{{{t = (-208 + 89.8)/-32) }}}

{{{t = -118.2/-32) }}}

{{{t=3.7sec}}}.........the rocket be 550 feet from the ground when it goes up

or

{{{t = (-208 - 89.8)/-32) }}}

{{{t = -297.8/-32) }}}

{{{t=9.3sec}}}........the rocket be 550 feet from the ground when it goes down after it reaches maximum height


(c) After how many seconds will the rocket strike the ground?


{{{0=-16t^2+208t}}}



{{{t = (-208 +- sqrt( 208^2-4*(-16)*0 ))/(2*(-16)) }}}


{{{t = (-208 +- sqrt( 43264 ))/-32) }}}


{{{t = (-208 +- 208)/-32) }}}


solution:

{{{t = (-208 + 208)/-32) }}}

{{{t = 0/-32 }}}

{{{t = 0 }}}

or

{{{t = (-208 - 208)/-32) }}}

{{{t = -416/-32) }}}

{{{t=13}}}.......the rocket strike the ground in {{{t=13sec}}}; on a graph, that will be a point ({{{13}}},{{{0}}})