falling objects

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mathhelper

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if a ball is thrown downward at 22 ft/per/sec from 65 feet how long will it take to reach the ground?

If it is thrown at the same speed from 100 feet how long will it take to reach 65 feet above the ground?

I am having trouble understanding the equation...
 
mathhelper said:
if a ball is thrown downward at 22 ft/per/sec from 65 feet how long will it take to reach the ground?

If it is thrown at the same speed from 100 feet how long will it take to reach 65 feet above the ground?

I am having trouble understanding the equation...
Click to expand...

Since the problem is talking about "reach the ground" - we are talking about earth's gravity.

Do you know Galileo's equations like:

s - s[sub:g367ajos]o[/sub:g367ajos] = ut + 1/2 * g * t[sup:g367ajos]2[/sup:g367ajos]

If not - then what equation/s have been taught to you regarding these types of problems.
 
I have learned how to figure an object falling from lets say 60 or 80 or 100 feet. formula is 60-16t^2=0 and then solve for t.


If we use a problem like the initial one and use the equation -16t^2-22t+65. here is where I become stuck because it does not seem like one can reduce this or simplify it. if a ball was thrown downward at 22ft/per/sec from 100 feet and I wanted to show my results symbolically at 65 feet do I use a differt equation?
 
mathhelper said:
I have learned how to figure an object falling from lets say 60 or 80 or 100 feet. formula is 60-16t^2=0 and then solve for t.


If we use a problem like the initial one and use the equation -16t^2-22t+65. here is where I become stuck because it does not seem like one can reduce this or simplify it. if a ball was thrown downward at 22ft/per/sec from 100 feet and I wanted to show my results symbolically at 65 feet do I use a differt equation?
Click to expand...

Do you know how to solve quadratic equations - like:

\(\displaystyle ax^2 \ \ + \ \ bx \ \ + \ \ c \ \ = \ \ 0\)
 
I can normally solve quadratic equations but this does not seem to work and give a number tht checks out.
 
\(\displaystyle S(t) \ = \ -16t^2+V_o(t)+S_o, \ distance \ formula \ where \ V_o \ = \ initial \ velocity \ and \ S_o \ = \ initial \ distance\)

\(\displaystyle Can \ you \ take \ it \ from \ here?\)
 
Thanks for the help. I can get to that point. I come up with 16t^2-22t+62. The problem comes when I try to simplify it.
Sorry the number was 62 not 65...

I can not figure out the (t-?)(t-?). Initially I came u with -2(8t^2-11t-32) is this what it means to show it symbollically?
 
\(\displaystyle 1) \ S(t) \ = \ ground \ level \ = \ 0 \ ft., \ V_0 \ = \ initial \ velocity \ = \ -22ft./sec, \ S_0 \ = \ initial \ distance\)

\(\displaystyle = \ 62 \ ft.\)

\(\displaystyle 2) \ S(t) \ = \ 62 \ ft., \ V_0 \ = \ -22ft./sec. \ and \ S_0 \ = \ 100 \ ft.\)

\(\displaystyle Now, \ just \ plugged \ the \ values \ into \ your \ distance \ formula \ and \ you \ are \ done.\)

\(\displaystyle For \ t, \ you'll \ get \ two \ values, \ discard \ the \ negative \ one \ as \ time \ isn't \ recorded\)

\(\displaystyle in \ negative \ time \ unless, \ perhaps, \ we \ are \ dealing \ with \ anti-matter.\)

\(\displaystyle Note: \ I \ am \ assuming \ that \ you \ are \ familiar \ with \ The \ Quadratic \ Formula.\)
 
When I am asked to determinee this symbollically then do I show this as 2(31t^2-11t+50)???
 
\(\displaystyle 1) \ S(t) \ = \ 0 \ = \ -16t^2-22t+62, \ solving \ for \ t, \ we \ get \ t \ \dot= \ 1.3976 \ sec.\)

\(\displaystyle 2) \ S(t) \ = \ 62 \ = \ -16t^2-22t+100, \ t \ = \ 1 \ sec. \ QED\)
 
that is great. Thanks for the help. One last question how did you get to that. I have severl problems like this and it would be a huge help to see the work so I can understand how to get to the result.
 
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