SOLUTION: Can someone please help me with this problem. I have tried working it but I do not understand it. Thank you in advance The height of a ball at time t is given by h=-16t^2 - 6t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can someone please help me with this problem. I have tried working it but I do not understand it. Thank you in advance The height of a ball at time t is given by h=-16t^2 - 6t       Log On


   

Question 3740: Can someone please help me with this problem. I have tried working it but I do not understand it. Thank you in advance
The height of a ball at time t is given by h=-16t^2 - 6t +32
a)What was the initial hegiht of the ball?
b)Approximately how long does it take for the ball to hit the ground?
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
this type of question is much easier if you have a grasp of physics - it is a physics question: the language of physics is maths, that is why it is here in a maths syllabus, as an application of quadratic equations. Anyway, follow my reasoning here as i cannot draw a good diagram.

Draw a simple n-shaped curve...more like a steep line up then arcing to come back down again. If i graph it, it looks like:

graph%28300%2C300%2C+-3%2C+3%2C+-2%2C+35%2C+-16x%5E2-6x%2B32%29
Draw a horizontal line to denote the ground. Now the first part implies that the ball was not thrown from the ground, but at some height above it. The INITIAL means when time = zero, as that is the start, so just let t=0. We therefore get:

h+=+-16t%5E2+-+6t+%2B+32

h+=+-16%280%29%5E2+-+6%280%29+%2B+32
ie h = 32. Easy enough?

Now for the slightly trickier concept. How long does it take to hit the ground? Well, h is the height of the ball and we now know that the initial height is 32. This implies that the ground is 32 lower. Yes? Now lower means -ve: this is the tricky point, so we put h=-32 into the equation now, to find the value(s) of t that this gives:

-32+=+-16t%5E2+-+6t+%2B+32
0+=+-16t%5E2+-+6t+%2B+64
0+=+-8t%5E2+-+3t+%2B+32 or re-arranging, we can say that 8t%5E2%2B3t-32+=+0. We now have a quadratic to solve. I don't think we can factorise this easily, so use the formula:

we get t+=+%28-3+%2B-+sqrt%289+-+4%288%29%28-32%29%29%29%2F16

t+=+%28-3+%2B-+sqrt%281033%29%29%2F16
so t+=+%28-3+%2B+sqrt%281033%29%29%2F16 or t+=+%28-3+-+sqrt%281033%29%29%2F16

t=1.82 (to 2dp) or t=-2-20.

Now, to me these values look wrong, but i have to go home now, so i cannot check the answer. Anyway, the method is correct. Ignore the negative time answer.. you want the 1.82 answer.

jon.