Question

A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=72t-16t^2. What is the maximum height that the ball will reach?
Do not round your answer

Answer 1

Answer:

The maximum height that the ball will reach is 81 ft

Step-by-step explanation:

Note that the tray of the ball is given by the equation of a parabola of negative main coefficient. Then, the maximum value for a parabola is at its vertex.

For an equation of the form

$at ^ 2 + bt + c$

So

the t coordinate of the vertice is:

$t =-\frac{b}{2a}$

In this case the equation is:

$h(t)=72t-16t^2$

So

$a=-16\\b=72\\c=0$

Therefore

$t =-\frac{72}{2(-16)}$

$t=2.25\ s$

Finally the maximum height that the ball will reach is

$h(2.25)=72(2.25)-16(2.25)^2$

$h=81\ ft$