Physics Help?

[iComessy]

I'm having a little trouble with this question. I know it's easy but I'm overthinking it and can't find the correct formulas

 

Q: A ball rolls horizontally off a table with an initial speed of 2.45m/s. The ball strikes the floor with a horizontal displacement from the table of 1.3m. Determine the height of the table.

 

[scobie56]

the funny thing is i just did this in school like a week ago and i forgot all ready 

[cortexcortex]

1.37 m

[Sauron]

the time it takes to reach 1.3 m from the falling position horizontally is 1.3/2.45 seconds. The distance it falls is given by the integral of the integral of the downwards acceleration relative to time, which is g*(t^2)/2.

[AresKrieger]

nvm

[Philosobyte]

1.3m / (2.45 m/s) = 0.530612 sec

 

1/2(9.8 m/s)(0.530612 sec)^2 = 1.37959m = 1.38m

 

Formula is distance = 1/2at^2

[Aytex]

my dad is physics professer, but im too lazy to go ask him

[iComessy]

1.3m / (2.45 m/s) = 0.530612 sec

 

1/2(9.8 m/s)(0.530612 sec)^2 = 1.37959m = 1.38m

 

Formula is distance = 1/2at^2

the time it takes to reach 1.3 m from the falling position horizontally is 1.3/2.45 seconds. The distance it falls is given by the integral of the integral of the downwards acceleration relative to time, which is g*(t^2)/2.

 

Ah yes! I was trying to do D=VT+1/2 AT^2, but couldn't rearrange because neither V or T was 0

Thanks so much!

[Tsuki]

e=mc^2

[Philosobyte]

Ah yes! I was trying to do D=VT+1/2 AT^2, but couldn't rearrange because neither V or T was 0

Thanks so much!

Starting from the beginning:

Since horizontal velocity does not change when an object falls, you can figure out the time it took to hit the ground by looking at the velocity and distance.

 

So now you can look at all the variables you have and need:

t = time = 0.530612 sec (just figured that out)

vi = initial velocity (which is zero because things have no vertical velocity when they start falling)

a = acceleration (which is 9.8 m/s due to gravity)

d = we need to find this one. 

 

So the formula you stated actually works - initial velocity is indeed zero. 

 

Then you just plug in and voila. 

[iComessy]

Starting from the beginning:

Since horizontal velocity does not change when an object falls, you can figure out the time it took to hit the ground by looking at the velocity and distance.

 

So now you can look at all the variables you have and need:

t = time = 0.530612 sec (just figured that out)

vi = initial velocity (which is zero because things have no vertical velocity when they start falling)

a = acceleration (which is 9.8 m/s due to gravity)

d = we need to find this one. 

 

So the formula you stated actually works - initial velocity is indeed zero. 

 

Then you just plug in and voila. 

I was trying to find the time with  D=VT+1/2 AT^2, but I just needed to do t=d/v

​So I was in fact overthinking it

[Ekpyrosis]

Let's try to describe the position of the ball as a function of time.
I'll set (0|0) as the point on the floor underneath the edge of the table.
The position on the x-axis can be described as x=2.45(m/s)*t as gravity doesn't affect horizontal movement and I assume we're ignoring friction.
The position on the y-axis can be described as y=h-4.9(m/s²)*t² while h is the heigh of the table. If you have trouble following, remember the formula for movement with constant acceleration.

Now we can eliminate t from our equations by rearrangin the first one and inserting the expression for t into the second. This leaves us with y=h-0.81632653061(1/m)*x²

With this function we can insert the coordinates for the point where the ball hits the floor (y=0, x=1.3m) and solve for h which gives us a result of roughly 1.38m.

 

Hope this was helpful.