Question 118894
{{{h= - 16t^2 + 48t + 2}}} Start with the given equation



{{{38= - 16t^2 + 48t + 2}}} Plug in h=38



{{{0=-16t^2+48t+2-38}}}  Subtract 38 from both sides. 



{{{0=-16t^2+48t-36}}}  Combine like terms



{{{0=-4(2t-3)(2t-3)}}} Factor the right side 



Now set each factor equal to zero:

{{{2t-3=0}}} or  {{{2t-3=0}}} 


{{{t=3/2}}} or  {{{t=3/2}}}    Now solve for t in each case



Since we have a repeating answer, our only answer is {{{t=3/2}}} (which is {{{t=1.5}}} in decimal form)


Notice if we graph {{{y=-16t^2+48t-36}}} we can see that the only root is {{{t=3/2}}}. So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, -16x^2+48x-36) }}}





-----------------------


Answer:

So it takes 1.5 seconds for the ball to reach 38 above the ground