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## #1 2006-03-13 04:05:52

bella
Guest

### help..

I was wondering if i can get some help solving this problem.. If a juggler can toss a ball into the air at a velocity of 64ft/sec from a height of 6 ft, then what is the max. height reached by the ball?

## #2 2006-03-13 05:28:25

gnitsuk
Member
Registered: 2006-02-09
Posts: 121

### Re: help..

You need to use two formula:

v = u + at

and

s = ut + at^2/2

Rearrange the first one to give:

t = (v - u) / a

Now convert your value of 64 ft/sec into metres per second and use this as the value of u in the formula.
a = -10 (gravity acting downwards gives -'ve sign, a is not exactly 10 but I'll use 10 here). Finally v = 0 (the final velocity of the ball at the top of the motion is zero).

Put these values into the formula to get a value for t (the time to get to maximium height) now use the second foumla to find a value for s (the distance travelled). Finally add 6ft to this.

That's it.

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## #3 2006-03-13 05:47:53

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

### Re: help..

Are you in Calculus, bella?  If so, then you just start out with:

a = -32ft/sec

Where a is acceleration.  Since gravity is always working on the ball, is constant, and is negative because it's "pushing" the ball downward, the acceleration is always -32.

Now we take this value and integrate it to get:

v = -32t + C.  Since v at t=0 is 64,

64 = -32(0) + C, and C = 64

so v = -32t + 64

Integrate again, and we find that:

s(distance) = -16t^2 + 64t + C

But we know that the distance at time 0 is 0:

0 = -16(0)^2 + 64(0) + C, C = 0

So s = -16t^2 + 64t

And we have just derived the equations that gnitsuk gave.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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