How far away will the ball land?

[1irishman]

Homework Statement

A ball rolls off an incline at a velocity of 22m/s. The angle of the incline is 32deg, and the height of the incline from the floor is 9m. Assume no air resistance.

Homework Equations

vf^2=vi^2+2ad
d=vit+1/2at^2

The Attempt at a Solution

I figured i should attempt to separate the motion of the ball into the x and y dimensions first so this was my attempt:
y motion
---------
22sin32*=11.7m/s
d=9m
vf=17.7m/s
a=-9.8
t=0.74

x motion
----------
vi=vf=18.7m/s because 22cos32=18.7m/s
t=0.74s

the answer is 11m, but i don't know how to get this answer...please help?

 

[Doc Al]

y motion
---------
22sin32*=11.7m/s
d=9m
vf=17.7m/s
a=-9.8
t=0.74

How did you solve for the time?

 

[1irishman]

time
-----
9=11.7t+1/2(-9.8)t^2
9=11.7t - 4.9t^2
-2.7/-4.9=.55
sqrt .55=.74s

 

[Doc Al]

time
-----
9=11.7t+1/2(-9.8)t^2

Careful: Check the sign of your 'd' and 'vi'.

 

[1irishman]

oops...I guess 'd' is -9 because it is pointing down? And 'vi' is -11.7 because of direction too?
I got a new time of .64s
If the above is correct, i still don't know how to solve this problem...help please? Thank you.

 

[Doc Al]

oops...I guess 'd' is -9 because it is pointing down? And 'vi' is -11.7 because of direction too?

Yes.

I got a new time of .64s

My answer is close to that.

If the above is correct, i still don't know how to solve this problem...help please?

Now consider the horizontal motion. You have the speed and the time.

 

[1irishman]

d=vt
So, d= (18.7)0.64
= 11.9m
Is that correct for distance?

 

[Doc Al]

d=vt
So, d= (18.7)0.64
= 11.9m
Is that correct for distance?

That's the correct method. My answer is a bit less; try doing the calculation with more accuracy until the end.

 

[1irishman]

Yes okay thank you, because it looks like the answer in the book is around 0.9 metres less than my value. How do i calculate with more accuracy throughout in the future please?

 

[Doc Al]

How do i calculate with more accuracy throughout in the future please?

Just carry all intermediate values with more digits. Round off only at the end. For example, instead of 22sin32 = 11.7, use 11.66. And so on.

 

[1irishman]

Just carry all intermediate values with more digits. Round off only at the end. For example, instead of 22sin32 = 11.7, use 11.66. And so on.

Thank you for all your help! I can see where my answers have been off marginally on previous problems due to rounding off the intermediate values too soon as it were.