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-   -   Determine the height of the Mountain.... (http://mymathforum.com/algebra/340256-determine-height-mountain.html)

 GIjoefan1976 April 29th, 2017 09:47 AM

Determine the height of the Mountain....

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I am doing number 2 a is the height of the moutian as easy as just the 500? Thanks

 skeeter April 29th, 2017 10:01 AM

yes ... height of the mountain is h(0) = 500 meters

 GIjoefan1976 April 29th, 2017 10:16 AM

Quote:
 Originally Posted by skeeter (Post 568655) yes ... height of the mountain is h(0) = 500 meters
Thanks Skeeter! If okay can I ask "c" is our starting point? so what are "a" and "b" I don't get where the get these numbers from?

 skeeter April 29th, 2017 10:32 AM

$a$ is the coefficient of the quadratic term, $a = -4.9$

$b$ is the coefficient of the linear term, $b = 196$

$c$ is the constant term, $c=500$

 GIjoefan1976 April 29th, 2017 10:46 AM

Quote:
 Originally Posted by skeeter (Post 568657) $a$ is the coefficient of the quadratic term, $a = -4.9$ $b$ is the coefficient of the linear term, $b = 196$ $c$ is the constant term, $c=500$

Okay, I think I messed up my words again... I guess I am just confused how they got the numbers? How did they know what numbers to put in for a and c? I am guessing it's because they already had the numbers?

Cause now they want me to plug in numbers for a b and c I think, but by writing a new.... Assuming its height is a quadratic function of time, how long will it spend in the air?

A ball is thrown into the air from 6 feet above the ground. It reaches its maximum height of 18 feet in 3 seconds

So I would think c=6

18 is maybe our b

and a is maybe our unknown?

 skeeter April 29th, 2017 11:00 AM

The general equation for projectile motion in one dimension is $h(t) = -\dfrac{1}{2}gt^2 + v_0 \cdot t + h_0$

in English units, $g = 32 \, ft/sec^2$

in metric units, $g = 9.8 \, m/sec^2$

Quote:
 Originally Posted by GIjoefan1976 (Post 568658) A ball is thrown into the air from 6 feet above the ground. It reaches its maximum height of 18 feet in 3 seconds
This problem is in English units (because height is given in feet)

$a = -16$

The $b$ value is the initial velocity of the projectile ... $b = v_0$

The $c$ value is the initial height of the projectile ... $c = h_0$

You are given $h(0) = 6 = c$ and $h(3) = 18$ ...

$18 = -16(3^2) + v_0(3) + 6$

Now you can solve for $b = v_0$ and determine the equation for height as a function of time.

 GIjoefan1976 April 29th, 2017 11:11 AM

Quote:

Originally Posted by skeeter (Post 568660)
The general equation for projectile motion in one dimension is $h(t) = -\dfrac{1}{2}gt^2 + v_0 \cdot t + h_0$

in English units, $g = 32 \, ft/sec^2$

in metric units, $g = 9.8 \, m/sec^2$

Quote:
 Originally Posted by GIjoefan1976 (Post 568658) A ball is thrown into the air from 6 feet above the ground. It reaches its maximum height of 18 feet in 3 seconds
This problem is in English units (because height is given in feet)

$a = -16$

The $b$ value is the initial velocity of the projectile ... $b = v_0$

The $c$ value is the initial height of the projectile ... $c = h_0$

You are given $h(0) = 6 = c$ and $h(3) = 18$ ...

$18 = -16(3^2) + v_0(3) + 6$

Now you can solve for $b = v_0$ and determine the equation for height as a function of time.

Hmm okay, so other than from you, where would I have learned that g equals 32? and to halve it as you have?

 skeeter April 29th, 2017 11:25 AM

Quote:
 Originally Posted by GIjoefan1976 (Post 568662) Hmm okay, so other than from you, where would I have learned that g equals 32? and to halve it as you have?
from ...

(a) your textbook if it has examples of these projectile motion problems

(b) your instructor if he/she did example problems in class

(c) yourself, if you did a web search ...

Quadratics in the real world

 GIjoefan1976 April 29th, 2017 08:55 PM

Quote:
 Originally Posted by skeeter (Post 568663) from ... (a) your textbook if it has examples of these projectile motion problems (b) your instructor if he/she did example problems in class (c) yourself, if you did a web search ... Quadratics in the real world
Okay thanks! Nope don't believe he ever said that 16 would always be our a...unless the problem gives us something for a? Really Super appreciate Your help and time!

 GIjoefan1976 April 30th, 2017 08:08 AM

going back to the original problem /application

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How come I am not coming up with a Decimal ?

Thanks

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