The height, h(t) in metres, of the trajectory of a football is given by h(t)= -4.9t +28t+2 where t is the time in flight, in seconds. Determine the maximum height of the football and the time when that height is reached.
+118724 I think that the first t is supposed to be squared
$$\\h(t)= -4.9t^2 +28t+2\\
h'(t)= -9.8t +28\\
$max height attained at the turning point ie when $\;\;h'(t)=0\\
-9.8t+28=0\\
-9.8t=-28\\
t=28/9.8\\
t\approx 2.857\;seconds\\$$
$${\mathtt{\,-\,}}{\mathtt{4.9}}{\mathtt{\,\times\,}}{{\mathtt{2.857}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{28}}{\mathtt{\,\times\,}}{\mathtt{2.857}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{41.999\: \!999\: \!9}}$$
Maximum height is approx 42 metres :)
+118724 I think that the first t is supposed to be squared
$$\\h(t)= -4.9t^2 +28t+2\\
h'(t)= -9.8t +28\\
$max height attained at the turning point ie when $\;\;h'(t)=0\\
-9.8t+28=0\\
-9.8t=-28\\
t=28/9.8\\
t\approx 2.857\;seconds\\$$
$${\mathtt{\,-\,}}{\mathtt{4.9}}{\mathtt{\,\times\,}}{{\mathtt{2.857}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{28}}{\mathtt{\,\times\,}}{\mathtt{2.857}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{41.999\: \!999\: \!9}}$$
Maximum height is approx 42 metres :)
