Mathematics: A model rocket is launched with an initial upward velocity of 188 ft/s. The rocket s height h (in feet) after t seconds is given by the following. h=188t-16t^2 Find all values of for which the rocket s height is 92 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the or button.)

The answer is 644Step-by-step explanation:23x4x7=644...

A model rocket is launched with an initial upward

jakhunter354

11.05.2021

0.51 and 11.24 seconds.

Step-by-step explanation:

The height h of a rocket with an initial upward velocity of 188 feet per second after t seconds is modeled by the function:

h(t)=188t-16t^2

And we want to find all values of t for which the rocket's height is 92.

So, we can set h(t) = 92 and solve for t:

92=188t-16t^2

We can divide everything by four:

23=47t-4t^2

Rearrange the equation:

4t^2-47t+23=0

We can use the quadratic formula:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

In this case, a = 4, b = -47, and c = 23. Substitute:

$\displaystyle x=\frac{-(-47)\pm\sqrt{(-47)^2-4(4)(23)}}{2(4)}$

Evaluate:

$\displaystyle x=\frac{47\pm\sqrt{1841}}{8}$

Hence, our two solutions are:

$\displaystyle x=\frac{47+\sqrt{1841}}{8}\approx 11.24\text{ or } x=\frac{47-\sqrt{1841}}{8}\approx0.51$

So, the rocket reaches a height of 92 feet after 0.51 seconds and again after 11.24 seconds.

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