Time Dilation. A group of scientists discover a new, rare isotope and are able to store a small amount of it. They determine that the isotope is unstable and half of their sample will decay in 13.0 monthsmonths . The scientists need a new laboratory to properly conduct measurements on the isotope. If laboratory is built before half the sample decays there will still be enough of the isotope available for experiments. However, it will take 21.0 monthsmonths to build the new lab. Fortunately, the scientists can quickly start construction and they have access to a spaceship that can travel at speeds approaching the speed of light c = 3.00

Answers

Answer 1

This question is incomplete, the complete question is;

Time Dilation. A group of scientists discover a new, rare isotope and are able to store a small amount of it. They determine that the isotope is unstable and half of their sample will decay in 13.0 months . The scientists need a new laboratory to properly conduct measurements on the isotope. If laboratory is built before half the sample decays there will still be enough of the isotope available for experiments. However, it will take 21.0 months to build the new lab. Fortunately, the scientists can quickly start construction and they have access to a spaceship that can travel at speeds approaching the speed of light c = 3.00 x 10⁸ m/s.

If they place their sample of the isotope on the spaceship, at what speed must it travel in order for the new laboratory to be completed on Earth by the time half of the isotope on the spaceship decays? Assume that it took one month for the scientists to actually start construction and launch the spaceship so half the sample will remain in 12.0 months but it will still take 21.0 months to build the new lab.

Answer:

the required speed is 2.4618 x 10⁸ m/s

Explanation:

Given the data in the question;

Time taken to complete a lab = 21 months  

it took them one one to actually start so

Time remaining so that sample only decays by 1/2 = (13 - 1) = 12 months

we need to find at what speed the spaceship should travel so that time on earth ( = 12 months) become time on spaceship ( = 21 months)

we make use of time dilation equation;

t' = t/√( 1 - v²/c² )

where t is time in rest frame = 12 and t' is time in moving frame = 21

so we substitute

21 = 12/√( 1 - v²/c² )

21√( 1 - v²/c² ) = 12

√( 1 - v²/c² ) = 12/21

we square both side

( 1 - v²/c² ) = ( 12/21 )²

( 1 - v²/c² ) = 0.3265

v²/c² = 1 - 0.3265

v²/c² = 0.6735

v² = 0.6735 × c²

v = √0.6735 × √c²

v = 0.8206 × c

given that speed of light c = 3 x 10⁸ m/s

v = 0.8206 × 3 x 10⁸ m/s

v = 2.4618 x 10⁸ m/s

Therefore, the required speed is 2.4618 x 10⁸ m/s


Related Questions

An inclined plane consists of a 25 m length that raises an object 5 m above the ground. When pushing a 4500 N crate to the top of the ramp you exert 1000 N. What is the ideal Mechanical Advantage of this machine?​

Answers

The IDEAL mechanical advantage of this ramp is (25m / 5m) = 5 .

But it's only giving you a real MA of (4500N/1000N) = 4.5 .

The friction between the crate and the surface of the ramp is robbing some of the work you do as you slide the crate up the ramp, which degrades the mechanical advantage.

An 5kg object is released from rest near the surface of a planet. The vertical position of the object as a function of time is shown in the graph. All frictional forces are considered to be negligible. What is the closest approximation of the weight of the object.
a) 300N
b) 30N
c) 5N
d) 150N

Answers

Answer:

The correct option is b: 30 N.

Explanation:

First, we need to find the acceleration due to gravity (a):

[tex] y_{f} - y_{0} = v_{o}t - \frac{1}{2}a(\Delta t)^{2} [/tex]   (1)

Where:

[tex]y_{f}[/tex]: is the final vertical position (obtained from the graph)

[tex]y_{0}[/tex]: is the initial vertical position (obtained from the graph)

v₀: is the initial speed = 0 (it is released from rest)

Δt: is the variation of time (from the graph)

From the graph, we can take the following values of height and time:

t₀ = 0 s → [tex]t_{f}[/tex] = 5 s

y₀ = 300 m → [tex]y_{f}[/tex] = 225 m

Now, by entering the above values into equation (1) and solving for "a" we have:

[tex] a = 2\frac{y_{0} - y_{f}}{(t_{f} - t_{0})^{2}} = 2\frac{300 m - 225 m}{(5 s - 0)^{2}} = 6 m/s^{2} [/tex]

Finally, the weight of the object is:

[tex] W = ma = 5 kg*6 m/s^{2} = 30 N [/tex]

Therefore, the correct option is b: 30 N.

I hope it helps you!                                                                                                            

What is the hottest planet in the milky way galaxy

Answers

Answer:

Venus

Explanation:

why type of volcano is built almost entirely from ejected lava fragments

Answers

Answer:

Shield volcanoes

Explanation:

a race car goes around a circular track of radius 150 m at speed of 10.0 m/s. How long does it take to complete one lap?

Answers

Answer:

94.25 seconds

Explanation:

Solve for period (T) using: v=(2*pi*r)/T

rearrange: vT=2*pi*r

rearrange: T=(2*pi*r)/v

Plug in values.

T=(2*pi*150)/10

T=94.25 seconds

If a race car goes around a circular track of a radius of 150 m at speed of 10.0 m/s ,then the time taken to complete the one lap would be 94.25 seconds.

What is speed?

The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object. The unit of speed is a meter/second. The generally considered unit for speed is a meter per second.

As given in the problem a race car goes around a circular track of radius 150 m at speed of 10.0 m/s.

vT = 2 × π × r

T = (2 × π × r)/ v

T = (2 × π× 150)/10

T = 94.25 seconds

Thus, the time taken to complete the one lap would be 94.25 seconds.

To learn more about speed here, refer to the link given below ;

https://brainly.com/question/7359669

#SPJ2

If a 15 N box is lifted a distance of 3 m, how much work is done?

0 J

45 J

5 J

5 N

Answers

Answer:

W=45J

Explanation:

W=Fd

W=15(3)=45

W=45J

Planets don't collide into
the sun because they

A. Are moving
B. Have too much mass
C. Have their own gravity
D. Are more attracted to each other

Answers

Every planet is at a different distance from the Sun and has a fixed orbit in which it revolves around the Sun. The Sun"s gravitational force holds the planets in this place and they do not collide with each other as their orbits are non-intersecting.
———
C. They have their own gravity

A wave with a frequency of 5Hz travels a distance of 40mm in 2 seconds.What is the speed of the wave​

Answers

Answer:

20mm per second

Explanation:

We intend to measure the open-loop gain (LaTeX: A_{open}A o p e n ) of an actual operational amplifier. The magnitude of LaTeX: A_{open}A o p e n is in the range of 106 V/V. However, the signal generator in measurement setup can supply minimal voltage of 1 mV, and the oscilloscope used at amplifier output can measure maximal voltage level of 10 V. Can you design a simple measurement setup using this signal generator and oscilloscope, and accurately measure the LaTeX: A_{open}A o p e n

Answers

Answer:

voltage divider,  R₂ = 1000 R₁

measuring the output in the resistance R₁

Explanation:

Let's analyze the situation, in an op amp in open gain loop, the gain is maximum G = 10⁶ V / V

in this case the signal generator gives a minimum wave of 1 10⁻³ V, after passing through the amplified it becomes 10³ V which saturates the oscilloscope.

To solve this problem we must use a simple voltage divider, for this we use the fact that in a series circuit the voltage is the sum of the voltages of each element.

If we use two resistors whose relationship is

            R₂ / R₁ = 10³

            R₂ = 1000 R₁

When measuring the output in the resistance R₁ we have the desired divider, with a tolerance range, for the minimum output of the generator (1 10⁻³V) we have a reading of V = 1 V in the oscilloscope, for which we can use voltage up to 10V on the generator

What is the gravitational potential energy of an object that has a mass of 8 kg and is 11.2 meters above Earth? Round your answer the nearest whole number.
A. 878 J
B. 30 J
C. 680 J

Answers

Answer:
A.
Explanation:
GPE= ham
GPE= (8)(11.2)(9.8)
GPE= 878.08
round it up
878 J

One of the smallest planes ever flown was the Bumble Bee II, which had a mass of 180 kg. If the pilot’s mass was 70 kg, what was the velocity of both plane and pilot if their momentum was 20,800 kg∙m/s to the west?

Answers

Answer:

83.2 m/s to the West

Explanation:

From the question given above, the following data were obtained:

Mass of plane = 180 Kg

Mass of pilot = 70 Kg

Momentum = 20800 Kg∙m/s West

Velocity =?

Next, we shall determine the total mass. This can be obtained as follow:

Mass of plane = 180 Kg

Mass of pilot = 70 Kg

Total mass =?

Total mass = Mass of plane + Mass of pilot

Total mass = 180 + 70

Total mass = 250 Kg

Finally, we shall determine the velocity. This can be obtained as follow:

Total mass = 250 Kg

Momentum = 20800 Kg∙m/s West

Velocity =?

Momentum = mass × Velocity

20800 = 250 × Velocity

Divide both side by 250

Velocity = 20800 / 250

Velocity = 83.2 m/s West

Thus, the velocity of both plane and pilot is 83.2 m/s to the West

what dose current equal?

Answers

There is a basic equation in electrical engineering that states how the three terms relate. It says that the current is equal to the voltage divided by the resistance or I = V/R. This is known as Ohm's law.

Hope this helps! :)

A storage tank has the shape of an inverted circular cone with height 15 m and base radius of 5 m. It is filled with water to a height of 11 m. Find the work required to empty the tank by pumping all of the water to the top of the tank. (The density of water is 1000 kg/m3. Assume g = 9.8 m/s2 is the acceleration due to gravity. Round your answer to the nearest integer.) g

Answers

Answer:

THE CORRECT ANSWER FOR THIS KS

Explanation:

STOP USING THIS APP FOR ANSWERS U KNOW NOTHING

Which of the following is NOT a reason
why gravity is important?

A It holds the planets in
orbit around the sun
B. It causes the ocean tides
C. It guides the growth of plants
D. None of the above

Answers

Answer:

I'm gonna say d

Explanation:

bc they all seem very important

hope this helped

Which statement best describes this situation

Answers

Answer:

what situation?

Explanation:

A physics student sits in a chair. The chair pushes up on the student's body. Identify the other force of the interaction force pair.

Answers

Answer:

gravity pulls down on student the chair pushes up on the student's body with the same force gravity is pulling down on the student

An object that is spinning, but not orbiting anything, has zero angular momentum.


True
False

Answers

The answer is fals:)

Which image best illustrates diffraction?

Answers

The one above I am guessing

Answer: A

Explanation:

What is the average kinetic energy of particles in a gas at a temperature of 245 Kelvins?

Answers

Answer:

2)

Explanation:

HELP me please cause I don't understand it.

Answers

Answer:

Force = 0.49 N (Approx)

Explanation:

Given:

Mass = 50 grams = 0.05 Kg

Acceleration = 9.81 m/s²

Find:

Force

Computation:

Force = Mass x Acceleration

Force = 0.05 x 9.81

Force = 0.4905

Force = 0.49 N (Approx)

Waves are ?
that can travel through matter.

Answers

Answer:

A wave can be thought of as a disturbance or oscillation that travels through space-time, accompanied by a transfer of energy. The direction a wave propagates is perpendicular to the direction it oscillates for transverse waves. A wave does not move mass in the direction of propagation; it transfers energy.

A physics student sits in a chair. The chair pushes up on the student's body. Identify the other force of the interaction force pair.

Answers

Answer:

The other force is the weight of the student.

Explanation:

With respect to Newton's third law of motion, for the student to sit and balance on the chair, there must be two equal and opposite forces involved. The student applies his/ her weight on the chair which acts downwards, while the chair applies an equal but opposite force to the weight of the student.

The force applied by the chair on the student's body is counter balanced by the student's weight. Note that, if the weight of the student is greater than the opposing force from the chair, the chair would collapse.

how many electrons can occupy each sublevel?

Answers

S sublevel can hold 2
P sublevel can hold 6
D sublevel can hold 10
F sublevel can hold 14

Which word best completes the sentence?

Select the word from the drop-down menu

He is quite
Choose...
despite never having left his smalL TOWEN

Answers

Answer:

it’s cosmopolitan

Explanation:

k12

Each vertical line on the graph is 1 millisecond (0.001 s) of time. What is the period and
frequency of the sound waves?

Answers

Explanation:

Given that,

Each vertical line on the graph is 1 millisecond (0.001 s) of time.

We need to find the period and the frequency of the sound wave. The period of a wave is equal to the each vertical line on graph i.e. 0.001 s.

Let f be the frequency of the sound wave. So,

f = 1/T

i.e.

[tex]f=\dfrac{1}{0.001 }\\\\f=1000\ Hz[/tex]

So, the period and the frequency of the sound waves is 1 milliseond and 1000 Hz respectively.

Is the speed of light constant throughout the universe.?

Answers

Answer:

It is a basic postulate of the theory of relativity that the speed of light is constant. This can be broken down into two parts: The speed of light is independent of the motion of the observer. The speed of light does not vary with time or place.

Explanation:

PLEASE CLICK ON THIS IMAGE I NEED HELP

Answers

Answer:

Second option

Explanation:

"Uniform" pretty much means the same thing happens.

4. When you are holding a book, energy is stored between the book and the Earth.
This type of energy is called
potential energy.
A. Elastic potential energy
B. Chemical potential energy
C. Gravitational potential energy
D. Kinetic energy

Answers

Answer:

gravitational potential energy

Which of the following is an example of an object with kinetic energy?
a. a plane lifting off of the runway
b. a bobsled perched at the top of a run
c. a snowball tumbling down a hill
d. both a and c

Answers

Answer:

A and C

Explanation:

Both have mass and are in motion

D is ur answer it should be right

A 50 kg mass is sitting on a frictionless surface. An unknown constant force called force A pushes the mass for 2 seconds until the mass reaches a velocity of 3 m/s. If the 50 kg mass is now pushed by an unknown force B and reaches the velocity of 3 m/s in 4 seconds, compare the impulse delivered to the mass when acted upon by force A with the impulse delivered to the mass when acted on by force B? *

A) The impulse delivered to the mass when acted upon by force A is greater
B) The impulse delivered to the mass when acted upon by force B is greater
C) The impulse is the same in each case
D) We need to know the value of force A and force B in order to determine this

Answers

Answer:

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