Word problem

Question

Ricky built a model rocket its flight can be modeled by the equation  h = -16 x² + 135 x, where H is the height of the rocket in feed after 2 seconds. About how long was Ricky's rocket in the air?

Answer 1

Normally, equations involving motion are written and graphed in terms of "height (h) and time (t)".  Your problem does involve these two quantities.  Height is a function of time. 

 

If we rewrote the equation in terms of these variables, you should recognize how to evaluate for the question asked. Let's assign...

h=height, in feet
t= time, in seconds

Let's rewrite your equation as a function...
h(t) = -16t²+135t.........height of rocket, in feet

We will solve for "t" when h(t)=0 or the height is zero....

-16t²+135t=0

t(-16t+135)=0

     t=0

     -or-

-16t+135=0

  -16t=-135

      t=8.44

 

So the rocket was in flight for approximately 8.44 seconds.  We solved for the "zeroes" of the motion quadratic where the parabola crosses the x-axis, or where the rocket flight path is at height equal to zero (first at launch where t=0 seconds and and when it hits the ground on the way down at t=8.44 seconds).

 

The graph of the above motion curve can be viewed at the following URL...

https://www.wyzant.com/resources/files/437617/parabolic_motion_graph