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Mama L [17]
2 years ago
11

Radioactive isotopes can be used to find the age of rocks, fossils, or other artifacts. Carbon-14 has a half-life of 5,730 years

. Suppose a sample of charcoal from a primitive fire pit contains one eighth of its original amount of carbon-14. How old is the sample?
Physics
1 answer:
bazaltina [42]2 years ago
8 0

Answer:

1/8 = (1/2)^3

This implies the sample has decayed for 3 half lives

3 * 5730 yrs = 17,200 years

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Given a particle that has the velocity v(t) = 3 cos(mt) = 3 cos (0.5t) meters, a. Find the acceleration at 3 seconds. b. Find th
DiKsa [7]

Answer:

a.\rm -1.49\ m/s^2.

b. \rm 50.49\ m.

Explanation:

<u>Given:</u>

  • Velocity of the particle, v(t) = 3 cos(mt) = 3 cos (0.5t) .

<h2>(a):</h2>

The acceleration of the particle at a time is defined as the rate of change of velocity of the particle at that time.

\rm a = \dfrac{dv}{dt}\\=\dfrac{d}{dt}(3\cos(0.5\ t ))\\=3(-0.5\sin(0.5\ t.))\\=-1.5\sin(0.5\ t).

At time t = 3 seconds,

\rm a=-1.5\sin(0.5\times 3)=-1.49\ m/s^2.

<u>Note</u>:<em> The arguments of the sine is calculated in unit of radian and not in degree.</em>

<h2>(b):</h2>

The velocity of the particle at some is defined as the rate of change of the position of the particle.

\rm v = \dfrac{dr}{dt}.\\\therefore dr = vdt\Rightarrow \int dr=\int v\ dt.

For the time interval of 2 seconds,

\rm \int\limits^2_0 dr=\int\limits^2_0 v\ dt\\r(t=2)-r(t=0)=\int\limits^2_0 3\cos(0.5\ t)\ dt

The term of the left is the displacement of the particle in time interval of 2 seconds, therefore,

\Delta r=3\ \left (\dfrac{\sin(0.5\ t)}{0.05} \right )\limits^2_0\\=3\ \left (\dfrac{\sin(0.5\times 2)-sin(0.5\times 0)}{0.05} \right )\\=3\ \left (\dfrac{\sin(1.0)}{0.05} \right )\\=50.49\ m.

It is the displacement of the particle in 2 seconds.

7 0
3 years ago
Janelle stands on a balcony, two stories above Michael. She throws one ball straight up and one ball straight down, but both wit
antoniya [11.8K]

Answer:

Both balls have the same speed.

Explanation:

Janelle throws the two balls from the same height, with the same speed. Both balls will have the same potential and kinetic energy. Energy must be conserved. When the balls pass Michael, again they must have the same potential and kinetic energy.

4 0
3 years ago
An atom with 4 protons, 5 neutrons, and 4 electrons has an atomic mass of _____ amu. (Enter a whole number.)
Oksi-84 [34.3K]
Atomic mass = number of protons + number of neutrons = 4+5 = 9 amu
6 0
3 years ago
A plane is flying due east with the velocity of 90m/s. The wind is blowing out of the north at 4m/s. What is the magnitude of th
Butoxors [25]
<span> as we know that the velocity vectors are at right angles
magnitude = ?
hypotenuse of a right triangle.
v^2 = 90^2 + 4^2
v^2 = 8116
Taking the square root of both sides here we get,
v = 90.1 m/s
hope it helps
</span>
4 0
3 years ago
Help please I have to turn this in tonight!!
inna [77]

Answer:

True

Explanation:

i searched it up and well this thing is making me do it up till 20 characters long so yea

3 0
3 years ago
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