How Do You Calculate the Time and Speed When a Ball Hits the Ground?

[calculusisfun]

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

Homework Statement

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.

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!

 

[rock.freak667]

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'.

 

[calculusisfun]

How do you know the acceleration is equal to 33?

 

[DarthBane]

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

 

[calculusisfun]

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

 

[DarthBane]

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.

 

[calculusisfun]

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

 

[DarthBane]

correct

 

[calculusisfun]

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. :)

 

[calculusisfun]

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 into 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? :)

 

[DarthBane]

yep, you are done.

 

[calculusisfun]

Cool, thanks a bunch