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Ratling [72]
3 years ago
6

A humanoid skeleton is found buried in the ashes of a volcano that erupted between 10,000 and 12,000 years ago. when scientists

use absolute dating techniques to obtain an age of the fossil, approximately how much carbon-14 isotope will remain?
Physics
2 answers:
Inga [223]3 years ago
5 0
From reliable sources in the internet, the half-live of carbon-14 is given to be 5,730 years. In a span of 10,000 to 12,000 years, there are almost or little more than 2 half-lives. Thus, there should be
                                           A(t) = A(0)(1/2)^t
where t is the number of half-lives, in this case 2. Thus, only about 1/4 of the original amount will be left. 
zmey [24]3 years ago
5 0

25% of the isotope will remain

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A) Time needed: 6.24 s

B) Time needed: 2.86 s

Explanation:

A)

In this part, we are told that the power if the engine is constant. The power of the engine is given by

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SInce power is constant, we can write:

\frac{\frac{1}{2}mv_1^2}{t_1^2}=\frac{\frac{1}{2}mv_2^2}{t_2}

where:

t_1=1.40 s is the time the car needs to accelerates to v_1=28.0 mph

t_2 is the time the car needs to accelerate to v_2=57.0 mph

Therefore, solving for t_2,

t_2 = \frac{v^2}{u^2}t_1=\frac{57^2}{28^2}(1.40)=6.24 s

B)

First of all, we have to calculate the acceleration of the car. We can do it using the following equation:

a=\frac{v-u}{t}

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u = 0 is the initial velocity

v=28.0 mph \cdot \frac{1609 m/mi}{3600 s/h}=12.5 m/s is the final velocity

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Substituting, we find the acceleration:

a=\frac{12.5-0}{1.40}=8.9 m/s^2

In this part, we are told that the force exerted by the engine is constant: according to Newton's second law, acceleration is proportional to the force,

F=ma

This means that the acceleration is also constant.

Now we want to find how long the car takes to accelerate to a final velocity of

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From an initial velocity of

u = 0

Using again the same suvat equation, and using the acceleration we found previously, we find:

t=\frac{v-u}{a}=\frac{25.5-0}{8.9}=2.87 s

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