Answer:
[tex]H=210.25\ \text{units}[/tex]
Step-by-step explanation:
Given that,
[tex]H = -16t^2 + 84t + 100[/tex] ...(1)
We need to find the maximum height
For maximum height, put dH/dt = 0
[tex]\dfrac{d(-16t^2 + 84t + 100)}{dt}=0\\\\-32t+84=0\\\\t=\dfrac{84}{32}\\\\t=2.625\ s[/tex]
Put t = 2.625 in equation (1)
[tex]H = -16(2.625)^2 + 84(2.625) + 100\\\\=210.25\ \text{units}[/tex]
Hence, the maximum height [tex]=210.25\ \text{units}[/tex]
