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a model rocket is launched from a roof into a large field. the path of the rocket can be modeled by the equation y= -0.06x^2 + 9.6+5.4 where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground.how far horizontally from it’s starting point will the rocket land? round your answer to the nearest hundredth

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SOLUTION

From the question, we are given the equation for the motion below

[tex]y=-0.06x^2+9.6x+5.4[/tex]

Since x, represents the horizontal distance, to get how far from the starting point the rocket land, we have to find the roots of the equation, that is the value of x. Graphing the function, we have

Now, from the graph, the curve cuts the x-axis at 160.561.

This is the horizontal distance of the rocket from the starting point.

Hence the answer is 160.56 to the nearest hundredth

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