# Math Help - An easy word question, but I can't quite get it =(

1. ## An easy word question, but I can't quite 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..

2. Originally Posted by Slipery
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..
Hi Slipery!

Part a)

You are correct! We disregard the other solution because it occurs before the kick, and is also a load of nonsense.

Part b)

Drawing a graph might help. What you are looking for is how long the graph of $y=-4.9t^2+10t+3$ stays above the graph of $y=5$. In other words, how long it is between points A and B. To do this we will solve and take the difference of the roots.

$-4.9t^2+10t+3=5$

$-4.9t^2+10t-2=0$

By the Quadratic Formula or otherwise:

$t = 0.225$ or $t= 1.816$

So the time the ball is above 5m is $1.816-0.225 = 1.591$ seconds.