The interval of time, the acorn moving through the air is t > 5/4.
A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
An acorn falls from the branch of a tree to the ground below = 25 feet
The equation is [tex]S(t) = -16t^2 + 25[/tex], where t is the number of seconds and
S is the distance.
At t=0,
⇒ [tex]S(0) = -16(0)^2 + 25[/tex]
⇒ [tex]S(0) = 25[/tex]
Initially, the acron is at 25 feet above the ground level. So t > 0, for the acron to fly on air.
The interval can be found as,
⇒ [tex]-16t^2 + 25 > 0[/tex]
⇒ [tex]-16t^2 > -25[/tex]
⇒ [tex]t^2 > \frac{25}{16}[/tex]
⇒ [tex]t > \sqrt{\frac{25}{16} }[/tex]
⇒ [tex]t > \frac{5}{4} or \frac{-5}{4}[/tex]
since t > 0, the interval is [tex]t > \frac{5}{4}[/tex]
Hence we can conclude that the interval of time, the acorn moving through the air is t > 5/4.
Learn more about word problems here
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