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#1 2006-11-25 21:35:51

needhelp2006
Member
Registered: 2006-11-25
Posts: 3

algebra ? (a word problem, everyones favorite)

A ball is hit upward from the top of an 80 foot building with an initial velocity of 64ft per second. The height (h) of the ball after t seconds of flight is given by the quadratic equation h=16t^2+64t+80

What is the height of the ball two seconds after its hit?
how long will it take for the ball to reach the ground?

can someone walk through this for me. I have several other questions like this to do so hopefully I will understand if I see how it is done. Your information/feedback is greatly appreciated.

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#2 2006-11-25 23:37:08

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: algebra ? (a word problem, everyones favorite)

I think your expression for h is wrong. In the one you have, all the terms are positive for t>0, and so the ball will just keep getting higher and higher, without ever falling down.

The t² coefficient has to be negative for the equation to describe projectile motion.

We can do the first part of the question though, even though the equation is flawed. To find the height at a certain time, you simply substitute in that time into the equation.

So at t=2, h = 16*2² + 64*2 + 80 = 272m.


Why did the vector cross the road?
It wanted to be normal.

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#3 2006-11-26 03:02:04

needhelp2006
Member
Registered: 2006-11-25
Posts: 3

Re: algebra ? (a word problem, everyones favorite)

you are right i forgot to place the negative sign in front of the 16. In what way will the change the equation.

h=-16t^2+64t+80

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#4 2006-11-26 03:11:57

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: algebra ? (a word problem, everyones favorite)

That looks a lot better.

So the first part can be solved in the same way as we did it before. Just replace any t you see with a 2 and work out what that gives.

h = -16*2² + 64*2 + 80 = 144m.

The second part wants you to find out at what time the ball hits the ground. It will do that when h=0, so you just need to solve the quadratic equation.

-16t² + 64t + 80 = 0
16t² - 64t - 80 = 0
t² - 4t - 5 = 0
(t-5)(t+1) = 0
t = 5 or -1. But because t cannot be less than 0, we only take the 5.

And that's the answer. The ball will hit the ground 5 seconds after it is launched.


Why did the vector cross the road?
It wanted to be normal.

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#5 2006-11-26 04:04:53

needhelp2006
Member
Registered: 2006-11-25
Posts: 3

Re: algebra ? (a word problem, everyones favorite)

Thank you very much. Hopefully this will help me with the rest of my assignment because the rest of the problems are just like this.

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