Answer:
[tex]Hmax=15.06[/tex] meters
Explanation:The question ask for the maximum value of the function f(t) which can be find by find the maxima of the function
The maxima of the function occurs when the slope is zero. i.e.
[tex]\frac{df}{dt} =0\\\frac{df}{dt} =\frac{d}{dt} (-4.9t^2+16t+2)\\\frac{df}{dt} =-4.9*2t+16\\-9.8t+16=0\\t=16/9.8\\t=1.63 secs[/tex]
Hence the maxima occurs at t=1.63 seconds
The maximum value of f is
[tex]f(1.63)=-4.9(1.63^2)+16(1.63)+2\\f(1.63)=15.06\\[/tex]
hence maximum height is found to be
[tex]Hmax=15.06[/tex] meters
