Story problem

Question

A projectile is launched upward with an initial velocity of 144feet/ second from the roof of a building. The height of a projectile (in feet) after t seconds is given by the function h(t)=-16tsquared+144t+50. What is the maximum height the projectile reaches?

Answer 1

Hi Tiphany down there in East Peoria...looks like you've got quite a few problems on your plate.

 

Ok, so you've got a function for height of a projectile after t seconds:

 

h(t) = -16t² +144t + 50

 

I'm going to assume that you're in a class like geometry, or algebra 2...not calculus.  :)

 

Here are some things to think about:

 

1.  What in the heck is h(t) a graph of?  That is, what shape is it?  It has a t-squared term in it, so it isn't a line.  :)  What is it?

 

2.  If you can figure out the answer to question 1...then how would you graph it?  You probably need to know some key points.  Or, there's a general equation you can use to graph it.  When you learned about lines, you probably learned that y=mx + b, and those letters "m" and "b" told you something about how to graph the line.  For h(t), what equation could you use to graph it?  How can you figure out the key points you need to know?  There are multiple ways to do it, and I don't know which way your teacher has suggested to you.

 

3.  On your graph, where is the point where the "maximum height" is reached?  Put a dot there.  What is that point called?

 

4.  If I'm asking for the "height" of a point on a graph, is that the x coordinate, or the y coordinate?

 

5.  If you can figure out which point you're looking for, and where that point is, and if you know you want the x or y coordinate to figure out the height of the projectile at its highest point...then you should have what you need.

 

Step 3 is probably the hardest, but if you can figure everything else out except that, let us know!

 

Hope this helps,

 

-- Michael