Answer:
h = 110.24 m
Step-by-step explanation:
It is given that,
A rock is thrown up from the ground at a velocity of 84 feet per second. The formula [tex]h = -16t^2 + 84t[/tex] gives the rock's height in feet after t second.
We need to find the maximum height of the rock. For maximum height put [tex]\dfrac{dh}{dt}=0[/tex]
So,
[tex]\dfrac{d( -16t^2 + 84t)}{dt}=0\\\\-32t+84=0\\\\t=\dfrac{84}{32}\\\\t=2.62\ s[/tex]
Put t = 2.62 s in the equation of height. So,
[tex]h = -16(2.62)^2 + 84(2.62)\\\\h=110.24\ m[/tex]
So, the maximum height of the rock is 110.24 m.
