Answer:
The maximum height of the watermelon is 74 feet.
Step-by-step explanation:
The watermelon reaches its maximum height when its velocity is zero. Mathematically speaking, velocity is the first derivative of the function height, that is:
[tex]v(t) = \frac{d}{dt} h(t)[/tex] (1)
Where [tex]v(t)[/tex] is the velocity, in feet per second.
If we know that [tex]h(t) = -16\cdot t^{2}+56\cdot t +25[/tex] and [tex]v(t) = 0\,\frac{ft}{s}[/tex], then the time associated with maximum height is:
[tex]v(t) = -32\cdot t +56[/tex] (2)
[tex]-32\cdot t + 56 = 0[/tex]
[tex]t = 1.75\,s[/tex]
Now we evaluate the function height at time found in the previous step: ([tex]t = 1.75\,s[/tex])
[tex]h(t) = -16\cdot t^{2}+56\cdot t +25[/tex]
[tex]h(1.75) = 74\,ft[/tex]
The maximum height of the watermelon is 74 feet.
