Question

A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t) = −4.9t2 + 24t + 10. How long does it take to reach maximum height? (Round your answer to three decimal places.)

Answer 1

Given:

The function is:

`h(t)=-4.9t^2+24t+10`

Find-:

The maximum height of function.

Explanation-:

The critical points:

`h(t)=-4.9t^2+24t+10`

The function derivative is;

`\begin{gathered} h(t)=-4.9t^2+24t+10 \\ \\ h^(\prime)(t)=-4.9*2t+24 \\ \\ h^(\prime)(t)=-9.8t+24 \end{gathered}`

The critical value of function is h'(t) = 0

`\begin{gathered} h^(\prime)(t)=-9.8t+24 \\ \\ h^(\prime)(t)=0 \\ \\ -9.8t+24=0 \\ \\ 9.8t=24 \\ \\ t=(24)/(9.8) \\ \\ t=2.45 \end{gathered}`

The maximum value is:

`\begin{gathered} h(t)=-4.9t^2+24t+10 \\ \\ h(2.45)=-4.9(2.45)^2+24(2.45)+10 \\ \\ h(2.45)=39.3878 \end{gathered}`

The maximum value is 39.3878