Question 97604
Well, you have given the of height (h) as a function of time (t) as:
{{{h(t) = -16t^2+v[0]t+h[0]}}} where {{{v[0] = 112}}}ft/sec, and {{{h[0] = 0}}}.
So what you are asking for is at what time, t, will h = 180 ft? Right?
Substituting h = 180, you can solve for t.
{{{180 = -16t^2+112t}}} Subtract 180 from both sides.
{{{-16t^2+112t-180 = 0}}} Simplify this by factoring a -4.
{{{-4(4t^2-28t+45) = 0}}} Factor trinomial in the parentheses.
{{{-4(2t-5)(2t-9) = 0}}} Apply the zero products principle.
{{{2t-5 = 0}}} or {{{2t-9 = 0}}} then:
{{{2t = 5}}} or {{{2t = 9}}} so...
{{{t = 2.5}}} or {{{t = 4.5}}}
The answer to the question..."At what time will the arrow reach a height of 180 ft?"
It will reach a height of 180 ft in 2.5 seconds on the way up and again at 4.5 seconds on the way down.