Calculating the Height of a Stadium Using Ball Drop: 2.29 Seconds & Speed

[thschica]

A ball is droped from a stadium.It hits the ground 2.29 seconds later.How high is the stadium?Do I use this equation?.5at^2(Thant is wrong isn't it?) How fast is the ball going when it hits the ground?(what equation do I use on this one?)

 

[TD]

I'm assuming no initial speed, then the height h is given by:

$$h = h_0 - \frac{{gt^2 }}{2}$$

Here, $h_0$ is the initial height, so what you are looking for. You choose h = 0, because that's where it hits the ground. Then fill in t and g and solve for $h_0$.

 

[thschica]

In this case would the answer be about 25.7 meters? And How do I tell How fast the marble is going?

 

[TD]

That seems to be correct yes.

For the other question, use a relation between acceleration, speed and time. If time is in s and acceleration in m/s², what would give speed (m/s)?

 

[thschica]

would that equation be the y='s one?

 

[TD]

I was thinking about v = at

 

[thschica]

I have another question.If something is dropped and hits the ground one second later how high is it? With that equation I got 7.1.Why is it not 9.8 meters?

 

[TD]

Because it's not the speed which is 9.8m/s but the acceleration which is 9.8m/s².
Are you sure you got 7.1 though?

 

[thschica]

No I got 4.9 sorry

 

[thschica]

Would the ball be going 22m/s before it hit the ground?

 

[TD]

No I got 4.9 sorry

That is correct.

You see, an acceleration of 9.8m/s² means that after a full second, the speed has increased 9.8m/s. So when dropping something with no initial speed, it only reaches the speed of 9.8m/s after the full second, so when it hits the ground in your example.

The avarage speed was 9.8/2 = 4.9, exactly what you found

Would the ball be going 22m/s before it hit the ground?

That seems correct, approximately.

 

[thschica]

Thank You so much TD

 

[TD]

No problem

 

[thschica]

Say someone threw the ball up and it didnt hit the ground until 3.53 seconds later how do I find out the ending velocity?What if it was thrown down and hit the ground 1.81 seconds later?

 

[TD]

Thrown up would require the initial height and thrown down the initial speed, unless there is none.

Perhaps someone else can help, I'm logging off. 2.50 AM here, good luck!