# Homework Help: A ball is thrown upward hard question?

1. Sep 9, 2010

### calculusisfun

A ball is thrown upward... hard question??

1. The problem statement, all variables and given/known data
A ball is thrown up from 64 feet above the ground with an initial velocity equal to 128 feet per second. Find when and with what speed the ball hits the ground.

3. The attempt at a solution
v = 128
anti derivative of velocity yields ---> 128x + c

since the initial height is 64, plug in (0, 64)

128(0) + c = 64

c = 64

position function ---> 128x + 64

solve for x, 128x + 64 = 0
x = -1/2

I got here and realize my answer doesn't make any sense. Any help would be much appreciated,

Thanks!

2. Sep 9, 2010

### rock.freak667

Re: A ball is thrown upward... hard question??

Your initial velocity = 128 ft/s.

Acceleration a = 33 ft/s2 (you can put the more accurate number).

Integrating w.r.t t yields v=33t+c

when t=0, v=128. Find 'c'.

Now integrate that again to get 'x'. The ball hits the ground when x=0, so find 't'.

3. Sep 9, 2010

### calculusisfun

Re: A ball is thrown upward... hard question??

How do you know the acceleration is equal to 33???

4. Sep 9, 2010

### DarthBane

Re: A ball is thrown upward... hard question??

the a is more accurately 32.185 ft/s^2, but that is the gravitational acceleration on earth.

5. Sep 9, 2010

### calculusisfun

Re: A ball is thrown upward... hard question??

Oh... I thought it was 9.8m/s2??? No? Sorry for bugging you guys haha

Oh, haha. You put it in meters. I see. :p

6. Sep 9, 2010

### DarthBane

Re: A ball is thrown upward... hard question??

that is the metric system, you are using english units. So they are both correct.

if you are in an engineering course you might want to keep the english system as a course requirement.

7. Sep 9, 2010

### calculusisfun

Re: A ball is thrown upward... hard question??

Okay, also, is it supposed to be negative because it is pushing down or no? :\

8. Sep 9, 2010

### DarthBane

Re: A ball is thrown upward... hard question??

correct

9. Sep 9, 2010

### calculusisfun

Re: A ball is thrown upward... hard question??

Thank you very much DarthBane, I'm going to work it out real quick (like one min) and if you could confirm that'd be awesome. :)

10. Sep 9, 2010

### calculusisfun

Re: A ball is thrown upward... hard question??

Ok, so I had the gravitational acceleration equal -32.174 ft/sec^2 because that's what wikipedia said haha, and here's what I did:

v = -32.174t + c
128 = -32.174(0) + c
c = 128

v = -32.174t + 128
integral of velocity ---> -32.174t^2/2 + 128t + c
-32.174^2/2 + 128t + 64

solve for this equal to zero and you get:

t = 8.42874
plug that in to the first equation and you get
-143.186

So, the ball hits the ground at 8.42874 seconds with a velocity of -143.186 ft/sec. Loook right? :)

11. Sep 9, 2010

### DarthBane

Re: A ball is thrown upward... hard question??

yep, you are done.

12. Sep 9, 2010

### calculusisfun

Re: A ball is thrown upward... hard question??

Cool, thanks a bunch