Question 380973
First, let's get the equation right!
{{{f(t) = -16t^2+72t}}}
1) The time to reach maximum height is given by:
{{{t[max] = -b/2a}}}
{{{t[max] = -72/2(-16)}}}
{{{t[max] = 9/4}}}seconds.
2) The maximum height can be found by substituting the time {{{t[max] = 9/4}}}seconds into the given equation.
{{{h[max] = -16t^2+72t}}} Substitute {{{t[max] = 9/4}}}
{{{h[max] = -16(9/4)^2+72(9/4)}}} Evaluate.
{{{h[max] = -16(81/16)+162}}}
{{{h[max] = 81}}}feet.
3) The time whe debris will hit the ground ({{{h = 0}}}) can be found by setting the given equation f(t)= 0 and solving for the time, t.
{{{-16t^2+72t = 0}}} Factor out a t.
{{{t(-16t+72) = 0}}} Now apply the zero product rule:
{{{t = 0}}} or {{{(-16t+72) = 0}}}
The {{{t = 0}}} solution is the initial condition.
{{{-16t+72 = 0}}} Subtract 72 from both sides.
{{{-16t = -72}}} Divide both sides by -16.
{{{t = 9/2}}}
{{{t = 4.5}}}seconds.