How High Was the Shelf If a Ball Rolls Off at 8m/s and Hits the Ground in 0.22s?

[PhilMTSU12]

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?

 

[pleasehelpme6]

You have to do it all in the Y-direction.

Vo = 0
t = 0.22
a = gravity

d=Vot+1/2at²

solve for d

 

[PhilMTSU12]

correction d= (8)(.22)+1/2(0)(.22²)
d= (8)(.22)
d= 1.76

 

[PhilMTSU12]

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

 

[Daft]

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)

 

[PhilMTSU12]

ok vert= .24 and horz=1.76

what do I do with these 2 distances

 

[Daft]

The vertical distance is the height of the shelf

 

[PhilMTSU12]

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?

 

[Daft]

You didn't really only need half, but since Vo = 0, then Vot = 0

so Vot+1/2at² = 0 + 1/2at²

 

[PhilMTSU12]

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

 

[Daft]

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?

 

[PhilMTSU12]

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

 

[Daft]

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

 

[PhilMTSU12]

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

 

[PhilMTSU12]

Does the final anwser look correct?