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.
The concept required to solve this problem is associated with potential energy. Recall that potential energy is defined as the product between mass, gravity, and change in height. Mathematically it can be described as

Here,
= Change in height
m = mass of super heroine
g = Acceleration due to gravity
The change in height will be,

The final position of the heroin is below the ground level,

The initial height will be the zero point of our system of reference,


Replacing all this values we have,



Since the final position of the heroine is located below the ground, there will net loss of gravitational potential energy of 10744.81J
Mass, m = 5890g
Change in temperature, θ = Final_temperature - Initial_temperature
= 315 - 462°C
= -147°C
Specific heat capacity of aluminum, c = 0.900 J/(g*K)
=mcθ
=5890g x 0.900 J/(g*K) x -147°C
=-779,247j
Answer would be C.
Answer:
a) 
b) 
c)
d) 
Explanation:
Given:
- mass of the astronaut,

- vertical displacement of the astronaut,

- acceleration of the astronaut while the lift,

a)
<u>Now the force of lift by the helicopter:</u>
Here the lift force is the resultant of the force of gravity being overcome by the force of helicopter.

where:
force by the helicopter
force of gravity


b)
The gravitational force on the astronaut:



d)
Since the astronaut has been picked from an ocean we assume her initial velocity to be zero, 
using equation of motion:



c)
Hence the kinetic energy:



Presume we are looking for the current:
V = IR
120 = I*360
120/360 = I
1/3 = I
I = 1/3 = 0.333..
Current ≈ 0.33 Ampere.