# Math Help - Easy question, but I can't get it =(

1. ## Easy question, but I can't get it =(

Hey guys! So I have been struggling with a word question for the past hour, and for some reason I can't solve it.. I'm pretty sure I remember doing this stuff last year in grade 10 too..

I used the quadratic equation, and I tried to change it to vertex form and manipulate it that way..

Here is the question:

8: A football player attempts a field goal by kicking the football. The ball follows the path modelled by the equation h = -4.9t² + 10t + 3, where h is the height of the ball above the ground in metres and t is the time since the ball was kicked in seconds.

a) After how many seconds does the ball reach the ground?
b) The ball must clear the uprights for the field goal to count. The uprights are approximately 5m high. How long does the ball stay above 5m in height?

Ok, so I got a, at least I think I did.. I used the quadratic equation and ended up with 2.3 seconds as my answer..
For b, I'm not sure what to do to figure this out.. Because when I just sub 5 into the equation I get the wrong answer.. I used my graphing calculator and I figured out that it is above 5m for about 1.5 seconds or so, but I have to do this algebraically

2. Ok, so I got a, at least I think I did.. I used the quadratic equation and ended up with 2.3 seconds as my answer..
Right. Good job

b) The ball must clear the uprights for the field goal to count. The uprights are approximately 5m high. How long does the ball stay above 5m in height?
You want h>5

so

-4.9t² + 10t + 3 > 5

-4.9t² + 10t - 2 > 0

Now you need to find the solutions of -4.9t² + 10t - 2 = 0, then find the length of time between them.

So, I got 4 seconds :/ Considering that the ball is only in the air for 2.3 seconds, this seems a little off.

I used the quadratic equation again to get my two possiblities.

it ended up being
(-10 +- Square root of -39.2)
-9.8

And my final answer from this was 4.

Any help?

4. The quadratic formula should be $x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}$

so the solutions are $\frac {-10 \pm \sqrt {60.8}}{-9.8}$

I think you must of missed out on the b^2 in the formula.