Question

the height , h(t) in metres of the trajectory of a football is  given by h(t) = 2+28t-4.9t^2, where t is the time in flight, in seconds . Determine the maximum height of thefootball and the time wehn the height is reached

Answer 1

to get this, we get the derivative of h(t) with respect to t, and equate it to zero:
h(t) = 2 + 28t - 4.9t^2
0 = 28 - 9.8t
9.8t = 28
t = 2.86 s
*note that the derivative of a function is the slope of the tangent line at the given point (in this problem, the point referred is the time, t, that we're solving). since the given equation is a parabola (concave downward), it has a maximum point, and at this point, the slope is zero (that's why we equate to zero)

hope this helps~ :)