Question 631807
As the pine cone falls, its downwards velocity increases linearly (starting from zero) at an acceleration of 32 ft/s^2 (32 ft per second every second).
In general, acceleration is represented by the letter {{{a}}}.
(The acceleration due to gravity on the surface of planet Earth is often represented by the letter {{{g}}}, and we know it is {{{g=3.2}}}{{{ft/s^2}}}).
The distance {{{d}}} traveled by an object starting at rest and accelerating at a constant acceleration {{{a}}} for a time {{{t}}} is given by
{{{d=at^2/2}}}
In this case, {{{d=gt^2/2}}}
We know {{{d=144}}} {{{feet}}}, we know {{{g=3.2}}}{{{ft/s^2}}}), and we want to know {{{t}}} , which we will get in seconds.
We can substitute first to get
{{{144=32t^2/2}}} and then solve.
{{{144=32t^2/2}}} --> {{{144*2=32t^2}}} --> {{{144*2/32=t^2}}} --> {{{9=t^2}}}
The solution that makes sense (we do not expect a negative time) is
{{{t=sqrt(9)}}} --> {{{t=3}}} --> {{{highlight(t=3)}}} seconds.