h = 16t(7 – t) + 10

Question

In the formula, h and t are defined as follows:
t = the time, in seconds, that has elapsed since the rocket was
launched
 h = the height, in feet, of the rocket above the ground at time t
Use the formula to answer the following questions.
a. Determine the highest the rocket will be from the ground. Show your
work.
b. How many seconds after the rocket was launched did it hit the
ground? Show your answer using at least two different
representations (equation, graph, table).

Answer 1

Dear Pearl,

     Your first step will be to determine the greatest height of the rocket (maximum height).

 

1.  Using the distributive property, simplify the equation, so that you can see what you have.

 

h= 16t(7-t)+10                             h= 112t-16t² +10    

 

Rewrite it in correct standard order:     -16t²+112t +10

 

2.  Think about the standard equation for a quadratic,  0= aX² +bX +C.  Find the values of "a,b," and "c" using the equation on number one.

 

a=-16                 b=112          c=10                 Use the equation, t=x=-b/2a,  to find the  "X" value of the vertex. 

 

Later, using the "X" value, you can find the "Y" of the vertex point (maximum point). 

 

t=-(112)/2(-16)   =       -112/-32  = ____       Now, substitute t=______into the equation below to find the maximum

 

height:

 

0= -16(t)² +112(t) +10    (I will let you finish this problem.)

 

 

Question #2:  How many seconds after the rocket was launched did it hit the ground?

 

(You need to find the second root, x-intercept.  This is when the height is zero.)

 

0= -16t²+112t +10

  You need to factor; however, it might make it easier if you divided every term by 2.      

 

0=-8t²+56t+5    You could use the quadratic equation to determine your time.

You should get t≅ _____        t=________    You want to use the positive time.

 

Put this equation, 0= -16t²+112t +10, into your graphing calculator, and graph it.  You can then transfer the graph onto graph paper.  Press 2nd GRAPH to see a table, which you can use as well.

If I have helped you, please give me a thumbs up.

                                                                                 Susan C.

 

                                                                              Graphing the Parabola

 

P.S: In order to graph  0= -16t²+112t +10, rewrite it like this,  Y= -16X²+112X +10, so "t=X." Next, enter

 

-16X²+112X +10 into the graphing mode, such as press "2nd   and  " Y= ."

 

(Remember that the negative sign is a negative (-), not a subtraction entry.  Go to the second function, WINDOW. Press it, top left function. Change your Y-Max to 225.  Just use your down arrow key to move to the Y-Max, and then enter 225.  This will allow you to see the maximum point on your calculator, the greatest height of the rocket. Now, you can make a rough sketch of the object by knowing the maximum point and the X-intercepts, one intercept is where the object hits the ground on the right side. If you want to graph the object, just go to the graphing calculator table, and find a couple of points to make a rough sketch.  Just press 2nd graph to see the table related to your parabola.  Where y=0, is the X-intercept.  You can also see the maximum point, highest "Y" value, before the rocket moves back towards the earth.   I hope this paragraph helps you.

                                                                                   Susan C.