Understanding a Formula

[angieelahh]

i was given a formula to use for a series of problems, but i dont understand how to use it. The formula is

 

D= 1/2gt^2

[ydoaPs]

It is the distance an object in free fall will fall for a given time.

[thedarkshade]

i was given a formula to use for a series of problems, but i dont understand how to use it. The formula is

 

D= 1/2gt^2

Yes. We we learned in school about his we were given the same thing but using different symbols. It looked (and looks) like this: [math]h=\frac{1}{2}gt^2[/math]. As far as I can recall, we used this formula when we discussed about free fall (the fall ob objects without initial velocity).

 

The way how we derive the formula goes like this:

[math]s=v_{0}t + \frac{1}{2}at^2[/math] this is for finding the distance.

And as during free fall there is no initial velocity, then [math]v_0=0[/math]

and a=g (g-gravitational acceleration), and s=h (h-height) then the equation looks like this: [math]h=\frac{1}{2} gt^2[/math], just like your equation.

 

 

And where to use it?

We were given a drill like this: "What is the height of out school given in meters?"

Everyone first thought that we were supposed to measure the school's height by using a meter, but his formula makes it easier. I just got to the top of our school, took something (an object) and threw it down. I also had a stopwatch with me. At the time I dropped the object, I started the stopwatch and when that object hit the ground I stopped the stopwatch. I think it was near 1.6s. And then plugged the data into equation and it came out like this"

 

[math]h=\frac{1}{2}gt^2=\frac{1}{2}9.81\frac{m}{s^2}\times (1.6s)^2[/math]

 

[math]h=\frac{1}{2}9.81\frac{m}{s^2} \times 2.56 s^2[/math]

 

[math]h=\frac{25.1136}{2}m[/math]

 

[math]h=12.5568m[/math]

 

And this was the school's height!

[MrMongoose]

Not necessarily.. It could be anything. What exactly are you struggling with?

[thedarkshade]

Not necessarily.. It could be anything

Yes, and I just told one example!

[angieelahh]

well the problem im trying to use that with is..im trying to find how fast im suppose to toss a ball into the air in order for it to remain there for a total time of 2s ...

 

so what im not getting is..how to use that particular formula to answer the question..and you know for "gt" g=gravity..right?? then what does t equal??

[Cap'n Refsmmat]

Then you need the entire equation:

[math]D = V_0t + \frac{1}{2}gt^2[/math]

The V₀ term is the initial velocity (how fast you toss it). You'll want D to be zero, because you're presumably tossing the ball in the air and catching it at the same height.

 

t = the total time elapsed. So t would be 2 for your situation.

[iNow]

Hi Angie - I don't know the answer to your question, but wanted to apologize. I just reread my response to you in the other thread and realized it may have came across as rude and short. I really didn't mean it that way, so I do apologize if that's how it came across.

 

 

Good luck with your questions.

[thedarkshade]

so what im not getting is..how to use that particular formula to answer the question..and you know for "gt" g=gravity..right?? then what does t equal??

Yes, g=gravity. And about t you can easily derive from the equation:

 

[math]D=\frac{1}{2}gt^2[/math] /multiply with 2 and you get:

 

[math]2D=gt^2[/math] /divide with g

 

[math]\frac{2D}{g}=t^2[/math] /put the square of the other side and finally:

 

[math]t=\sqrt{\frac{2D}{g}}[/math]

Check the unit, it's s, it fits.\

 

 

Cheers,

Shade

[Royston]

Just to clarify for angieelahhs benefit, as t is already known ( 2 s ) then you need to rearrange the entire equation (see Capn's post) to make Vo the subject. That will give you, how fast the ball needs to be thrown to be airbourne for 2 seconds.

[swansont]

mod note: Posts removed

 

Don't give the answers, folks. This is HW Help, not Do-my-HW-for-me.

[thedarkshade]

That's my second.

 

Sorry:doh:

[iNow]

Don't give the answers, folks. This is HW Help, not Do-my-HW-for-me.

 

Oohhh... Where's THAT forum? I want to post my questions THERE!

[swansont]

Oohhh... Where's THAT forum? I want to post my questions THERE!

 

Subscriber-only. Got a credit card?

[Country Boy]

well the problem im trying to use that with is..im trying to find how fast im suppose to toss a ball into the air in order for it to remain there for a total time of 2s ...

 

so what im not getting is..how to use that particular formula to answer the question..and you know for "gt" g=gravity..right?? then what does t equal??

 

I think what you are asking is not "how do I solve for t", but "what does t mean". Let me point out that it is not enough to just learn "formula" if you don't learn, at the same time, exactly what each of the symbols represents! Here, "t" represents the TIME. Exactly what number that is depends on on where YOU decide t= 0 to be. Normally, it is best to choose t= 0 at the beginning- when the object is let fall or thrown.

 

By the way, I really hate it when people say something like "g= gravity". "Gravity" (and THAT really should be "the force of gravity) is a force while g is acceleration. That is "shorthand" for "g is the acceleration of a body due to gravity, at the surface of the earth". And shorthand can be very confusing.

 

Cap'h Refsmmat gave an excellent analysis of your problem. Go back and look at that.