Answered

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 + 7. How long does it take to reach maximum height?

Answer :

Given:

There are given the equation:

[tex]h(t)=-4.9t^2+24t+7[/tex]

Explanation:

According to the concept:

For any quadratic function:

[tex]f(x)=ax^2+bx+c[/tex]

With the negative leading coefficient, it gets the maximum at:

[tex]x=-\frac{b}{2a}[/tex]

So,

Apply the above formula to the given question.

Then,

From the given function:

[tex]h(t)=-4.9t^{2}+24t+7[/tex]

Where,

[tex]\begin{gathered} a=-4.9 \\ b=24 \end{gathered}[/tex]

Then,

Put the all values into the given formula:

So,

[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=-\frac{24}{-2(4.9)} \\ x=\frac{24}{9.8} \\ x=2.45 \end{gathered}[/tex]

Final answer:

Hence, it will take 2.45 seconds to get the maximum height.

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