Question

Brynn and Denise launch their rockets at the same time. The height of Brynn’s rocket, in meters, is given by the function f(x)=-4.9x^2+75x , where x is the number of seconds after the launch.

The height of Denise’s rocket, in meters, is given by the function
g(x)=_4.9x^2+50x+38
,  where x is the number of seconds after the launch.
There is a moment when the rockets are at the same height.
 
What is this height?
Enter your answer, rounded to the nearest tenth of a meter, in the box.

Answer 1

Answer: 102.7 meters

Explanation:

Given: Brynn and Denise launch their rockets at the same time.

The height of Brynn’s rocket, in meters, is given by the function
`f(x)=-4.9x^2+75x` , where x is the number of seconds after the launch.

The height of Denise’s rocket, in meters, is given by the function

`g(x)=-4.9x^2+50x+38`, where x is the number of seconds after the launch.

The moment when both rockets are on same height, then
`f(x)=g(x)`

`\Rightarrow-4.9x^2+75x=-4.9x^2+50x+38\\\\\Rightarrow\ 75x=50x+38\\\\\Rightarrow\ 25x=38\\\\\Rightarrow\ x=1.52`

It means at 1.52 seconds the rockets are at the same height.

To calculate the height substitute, the value of x in any of the function.

`f(1.52)=-4.9(1.52)^2+75(1.52)=102.67904\approx102.7` meters

Answer 2

The height of rocket is 102.7 meter.

Explanation:

Given : Brynn and Denise launch their rockets at the same time.

The height of Brynn’s rocket, in meters, is given by the function
`f(x)=-4.9x^2+75x` , where x is the number of seconds after the launch.

The height of Denise’s rocket, in meters, is given by the function

`g(x)=-4.9x^2+50x+38`, where x is the number of seconds after the launch.

There is a moment when the rockets are at the same height.

To find : The height

Solution :

When the rockets have same height

So,
`f(x)=g(x)`

`-4.9x^2+75x=-4.9x^2+50x+38`

`-4.9x^2+75x+4.9x^2-50x=38`

`25x=38`

`x=(38)/(25)`

`x=1.52`

Now, we put x value in any of the function to find height.

`f(x)=-4.9x^2+75x` , x=1.52

`f(x)=-4.9(1.52)^2+75(1.52)`

`f(x)=-11.32096+114`

`f(x)=102.67`

Nearest tenth = 102.7

Therefore, The height of rocket is 102.7 meter.