Question 1206277

 {{{h(t) = -4.9t^2 + 19.6t + 58.8 }}}

1. Use the function to predict the height of the object after one second? 

{{{t = 1}}}
{{{h(1) = -4.9*1^2 + 19.6*1 + 58.8}}}
{{{h(1) = 73.5}}}


2. Plug the function into Desmos. How many seconds will it take for the object to land? 

{{{h(t) = 0}}}

 {{{-4.9t^2 + 19.6t + 58.8 =0}}}

https://www.desmos.com/calculator

or

{{{ graph( 600, 600, -10, 10, -10, 80, -4.9x^2 + 19.6x + 58.8) }}} 


from the graph we see {{{h(6) = 0}}} and {{{h(-2) = 0}}} (disregard {{{t=-2}}}, time cannot be negative)

it will take {{{6 }}}seconds for the object to land


3. How long does it take for the object to reach its maximum height? How high does it go?

find first derivative and equal to zero

{{{h}}}'{{{(t)= -4.9*2t + 19.6=-9.8 t+ 19.6}}}

{{{-9.8 t+ 19.6=0}}}

{{{19.6=9.8t}}}

{{{t=19.6/9.8 }}}

{{{t =2}}}

it will take {{{2}}} sec for the object to reach its maximum heigh

{{{h(2) = -4.9*2^2 + 19.6*2 + 58.8}}}
{{{h(2) = 78.4 }}}meters


2. The object lands after {{{6}}} seconds.

3. The max height is {{{78.4}}} meters and it occurs at {{{t=2}}} seconds.