A ball rolls off a table

  • Thread starter PhilMTSU12
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In summary, a ball rolls off a table with a horizontal velocity of 8m/s and takes 0.22s to hit the floor. Using the equation d=Vot+1/2at², the height of the shelf can be calculated to be 1.76m. For the second problem, a table with a height of 2.8m is given and using the same equation, it takes the ball 0.756s to hit the ground and the horizontal distance from the base of the shelf is 6.048m.
  • #1
PhilMTSU12
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Homework Statement


A ball rolls off a table with a horizontal v of 8m/s. If it takes the ball .22s to hit the floor, how high was the shelf?


Homework Equations


d=Vot+1/2at²


The Attempt at a Solution


HORIZ
a=0
Vo=8m/s
V=8m/s
d=?
t=.22s

d= (8)(.22)+1/2(8)(.22²)

Is the hieght of the shelf d=1.997m?
 
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  • #2
You have to do it all in the Y-direction.

Vo = 0
t = 0.22
a = gravity

d=Vot+1/2at²

solve for d
 
  • #3
correction d= (8)(.22)+1/2(0)(.22²)
d= (8)(.22)
d= 1.76
 
  • #4
ok Vertical
a= -9.8m/s
Vo=0
V=?
d=9.8m
t=.22

(9.8)(.22)+1/2(9.8)(.22²)
d= 2.39
 
  • #5
PhilMTSU12 said:
ok Vertical
a= -9.8m/s
Vo=0
V=?
d=9.8m
t=.22

(9.8)(.22)+1/2(9.8)(.22²)
d= 2.39

Recheck your working, you made a mistake

Your equation there is:

at+1/2at2 instead of Vot+1/2at2

its just 1/2(9.8)(.222)
 
  • #6
ok vert= .24 and horz=1.76

what do I do with these 2 distances
 
  • #7
The vertical distance is the height of the shelf
 
  • #8
so, I only needed to find the vertical distance? I did the horz distance for no reason...

and why do i only need half of the equation?
 
  • #9
You didn't really only need half, but since Vo = 0, then Vot = 0

so Vot+1/2at2 = 0 + 1/2at2
 
  • #10
ok...
The next problem is this

A ball rolls off a table which is 2.8m high. If it leaves the table with a horizontal v of 8m/s, calc the distance from the base of the shelf at which the ball will strike the ground.

I know i need to figure out how long it will take the ball to strike the ground. then use that to find the horz distance

vert d= 1.41

8(1.41)= 11.28m
 
  • #11
You're theory is right, but your answer confuses me, what is that?

How are you finding the time the ball takes to hit the ground?
 
  • #12
i tried to quickly do all the work haha

vert distance
a= -9.8m/s
Vo=0
V=?
d=9.8m
t=?

using at+1/2at²

9.8= 1/2(9.8)t²

2(9.8)=9.8t²
over
9.8=9.8
(the 9.8's cancel leaving)

2=t²

t=square root of 2

t= 1.41


soo it will take 1.41s for the ball to hit the ground.

using t= 1.41 i can now find the horz distace

a=0
Vo=8
V=8
d=?
t=1.41

d= Vot

8(1.41)= 11.28m
 
  • #13
Well, your method of working is correct, but in the very beginning you used the wrong value of d

"A ball rolls off a table which is 2.8m high" not 9.8 like you used
 
  • #14
ok

2.8m= 1/2(9.8)t²

2(2.8)=2(1/2)(9.8)t²

5.6m= 9.8t²
Divide 9.8 to both sides

.5714=t²

t=.756s

d=Vot
d=8(.756)
d=6.048
 
  • #15
Does the final anwser look correct?
 

What causes a ball to roll off a table?

A ball may roll off a table due to the force of gravity pulling it downward, an uneven surface causing it to roll in a certain direction, or a push or nudge from an external force.

What is the velocity of a ball rolling off a table?

The velocity of a ball rolling off a table depends on various factors such as the height of the table, the angle at which it falls, and the surface it is rolling on. It can be calculated using the equation v = √2gh, where v is the velocity, g is the acceleration due to gravity, and h is the height of the table.

Can a ball roll off a table without any external force?

No, a ball cannot roll off a table without any external force acting on it. This is because of the law of inertia which states that an object at rest will remain at rest unless acted upon by an external force.

How does the height of the table affect the distance a ball rolls off?

The height of the table directly affects the distance a ball will roll off. The higher the table, the longer the distance the ball will travel before hitting the ground, due to the increased potential energy it gains from being at a higher position.

What is the impact of surface friction on a ball rolling off a table?

Surface friction can affect the speed and direction of a ball rolling off a table. A surface with high friction will slow down the ball's movement, causing it to roll a shorter distance. A surface with low friction will allow the ball to roll further and at a higher speed.

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