Answer:
Step-by-step explanation:
I don't know if you are a calculus student, but since calculus is the easiest way to solve this, that's what I used. The position equation is
[tex]s(t)=-6t^2+24t+14[/tex]
and the velocity function, the first derivative, is
[tex]v(t)=-12t+24[/tex]
From Physics, you should know that the velocity of an object is 0 at its highest point. That means that if we sub in a 0 for the velocity and solve for t, we find the time at which the object is at its highest point. That is:
[tex]0=-12t+24[/tex] and
[tex]0=-12(t-2)[/tex]
By the Zero Product Property,
-12 definitely does not equal 0, so that means that
t - 2 = 0 and
t = 2 seconds.
So at 2 seconds, the object is at its highest point. Go back to the position function now and sub in a 2 for t to find the height of the object at 2 seconds.
[tex]s(2)=-6(2)^2+24(2)+14[/tex] so
s(2) = 38 meters
