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marusya05 [52]
3 years ago
9

After a plant or animal dies the 14C content decreases with a half-life of 5730 years. If an archaeologist finds an ancient fire

pit containing partially consumed firewood, and the 14C content of the wood is only 15.5% that of an equal carbon sample from a present-day tree, what is the age (in years) of the ancient site?
Physics
1 answer:
Shalnov [3]3 years ago
6 0

Answer:

age of the site is 15411.75 years old

Explanation:

Given data

plant or animal dies = 14C

time period = 5730 year

carbon = 15.5%

to find out

age (in years) of the ancient site

solution

we know that Final value = Initial value  × 0.5^{n}

here n is half life passed

so for 15.5%

15.5% = 100% of  0.5^{n}

0.155 = 1 × 0.5^{n}

now take log both side

log 0.155 = log  0.5^{n}

n = log 0.155 / log 0.5

n = 2.68966

we know here  5730 years in half life

so for 2.68966 half-lives = 2.68966 × 5730  =  15411.7518

age of the site is 15411.75 years old

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Based on observations, the speed of a jogger can be approximated by the relation v 5 7.5(1 2 0.04x) 0.3, where v and x are expre
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Answer:

solution:

to find the speed of a jogger use the following relation:  

V

=

d

x

/d

t

=

7.5

×m

i

/

h

r

...........................(

1

)  

in Above equation in x and t. Separating the variables and integrating,

∫

d

x

/7.5

×=

∫

d

t

+

C

or

−

4.7619  

=

t

+

C

Here C =constant of integration.   

x

=

0  at  t

=

0

, we get:  C

=

−

4.7619

now we have the relation to find the position and time for the jogger as:

−

4.7619  =

t

−

4.7619

.

.

.

.

.

.

.

.

.

(

2

)

Here

x  is measured in miles and  t  in hours.

(a) To find the distance the jogger has run in 1 hr, we set t=1 in equation (2),    

     to get:

      = −

4.7619  

      =  

1

−

4.7619

      = −

3.7619

  or  x

=

7.15

m

i

l

e

s

(b) To find the jogger's acceleration in   m

i

l

/

differentiate  

     equation (1) with respect to time.

     we have to eliminate x from the equation (1) using equation (2).  

     Eliminating x we get:

     v

=

7.5×

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      a

=

d

v/

d

t

       =

−

0.675

/

      At  

      t

=

0

      the joggers acceleration is :

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−

0.675

m

i

l

/

        =

−

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×

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t

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4.7619

(

1

−

(

0.04

×

6  )

)^

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/

10=

t

−

4.7619

         or

         t

=

0.832

h

r

s

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