# Quadratic Word Problems

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• Sep 23rd 2007, 08:28 AM
justine_0612
Quadratic Word Problems
a flare is fired upwards from the deck of a chip. The flar hits the water. The height of the flare, h, in metres, above the water t seconds is given by the function h= -4.9t^2 + 98t + 8

a. How long does it take the flare to hit the water?
b.How high is the deck of the ship above the water?

I calculated the height of the flare as 498m through completing the square, and i calculated the time to reach maximum height as 10 seconds. But now I'm stuck.

Can anyone help me plz!!
• Sep 23rd 2007, 09:04 AM
topsquark
Quote:

Originally Posted by justine_0612
a flare is fired upwards from the deck of a chip. The flar hits the water. The height of the flare, h, in metres, above the water t seconds is given by the function h= -4.9t^2 + 98t + 8

a. How long does it take the flare to hit the water?
b.How high is the deck of the ship above the water?

I calculated the height of the flare as 498m through completing the square, and i calculated the time to reach maximum height as 10 seconds. But now I'm stuck.

Can anyone help me plz!!

Well, when is the flare at the water level? Solve
$-4.9t^2 + 98t + 8 = 0$

As to how high the deck of the ship is, when is the flare at the ship? Plug this time into your height equation and that will tell you how high the deck is.

-Dan
• Sep 23rd 2007, 09:06 AM
justine_0612
i understand that. bt i dont know how to
• Sep 23rd 2007, 09:17 AM
topsquark
Quote:

Originally Posted by justine_0612
i understand that. bt i dont know how to

Quote:

Originally Posted by topsquark
Well, when is the flare at the water level? Solve
$-4.9t^2 + 98t + 8 = 0$

I presume you are saying you don't know how to solve the quadratic.

When all else fails, use the quadratic formula:
$\text{If } ax^2 + bx + c = 0 \text{ then }x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For this problem we have that a = -9.8, b = 98, and c = 8.

You will have two answers as a result for the time. One of these will be negative, and thus is an unphysical solution and may be discarded.

-Dan
• Sep 23rd 2007, 09:35 AM
justine_0612
kk i got all that
thank you
• Sep 23rd 2007, 09:43 AM
Sean12345
I think you have made the question more complicated then it actually is (i think meaning that i may be in the wrong)

a) How long does it take to reach the water i.e. h = 0
-4.9t^2+98t+8 = 0
t = (-98+squareroot(98^2-(4*-4.9*-8))/(2*-4.9),
t = (-98-squareroot(98^2-(4*-4.9*-8))/(2*-4.9)
t = -0.08130215107
t = 20.08130215, therefore time to reach 0 metres i.e. water, i 20.08130215 seconds as time cant be negative.

b) How high is the Deck? Just use t = 0 seconds i.e. the flare hasnt left the deck yet.
h = -4.9(0^2)+98(0)+8
h = 8m

I think this is right, someone please correct me if im wrong.

Hope this helps, Sean.