(a) Find the value of γ for the following situation. An Earthbound observer measures 23.9 h to have passed while signals from a high-velocity space probe indicate that 24.0 h have passed on board. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Q: What must be the speed of an electron for its relativistic kinetic energy to be equal to its rest…

A: The relativistic kinetic energy (KE) of the electron is equal to the rest energy (E).

Q: A spacecraft is launched from the surface of the Earth with a velocity of 0.600c at an angle of…

A: Given: The velocity v1 = 0.6c, The velocity v2 = 0.7c, Angle of velocity v1 with x axis = 50.0

Q: The astronaut whose heart rate on Earth is 60 beats/min increases his velocity to v = 0.75 c. Now…

A:

Q: Show that for any relative velocity v between two observers, a beam of light projected by one…

A:

Q: The elementary particle called a muon is unstable and decays in about 2.20μs, as observed in its…

A:

Q: A space traveler takes off from Earth and moves at speed 0.9900c toward the star Vega, which is…

A:

Q: Two neutron stars are separated by a distance of 1.0 x 1011 m. They each have a mass o are initially…

A: Given:- The separation distance between the two neutron stars r= 1.0 x 1011 m  They have a mass m =…

Q: The origins of two frames coincide at t = t' 0 and the relative speed is 0.991c. Two micrometeorites…

A: t=277μS x=83500 m

Q: A space traveler takes off from Earth and moves at speed 0.9700c toward the star Vega, which is…

A: in this question  we use simple space motion equation  and get answer.

Q: If a spaceship is approaching the Earth at 0.100c and a message capsule is sent toward it at 0.100c…

A: Speed of the capsule relative to the ship using velocity addition theorem.

Q: To whom does the elapsed time for a process seem to be longer, an observer moving relative to the…

A:

Q: A spacecraft is measured to be 250.00 m long while it is at rest with respect to earth-based…

A: GivenLength of spaceship at rest with respect to observer, Lo=250 mSpeed of spaceship, v=0.8 c

Q: A spacecraft with a proper length of 250 m passes by an observer on the Earth. According to this…

A: proper length (Lo) = 250 m Let the speed of spacecraft = v time taken to pass a point as observed by…

Q: Suppose an astronaut is moving relative to the Earth at a significant fraction of the speed of…

A: The astronaut is moving relative to the earth. So, the earth is also moving relative to the…

Q: The rest energy and total energy, respectively, of three particles, expressed in terms of a basic…

A: Order of decreasing rest mass

Q: In an Earth reference frame, a star is 49 light-yearsaway. How fast would you have to travel so that…

A: If particle or an object travel at relativistic speed its length contraction occurs. Formula of…

Q: Many expressions in special relativity contain the gamma (y) factor. 1 Y = √1-v²/c² In the equation,…

A: The gamma factor is expressed as follows. γ=11-v2c2

Q: The origins of two frames coincide at t = t' 0 and the relative speed is 0.993c. Two micrometeorites…

A:

Q: A spacecraft with a proper length of Lp passes by an observer on the Earth. According to this…

A: It is known that when an object moves in high speed with respect to an observer then its length…

Q: Calculate the speed of a proton(m=1.67 x10-27kg)whose kinetic energy is exactly half (a) its total…

A: Given: Mass of the proton = 1.67 x10-27 Kg

Q: An astronaut traveling at a speed of 0.75c requires 25 years, as measured on Earth, to make a round…

A: given: velocity v=0.75 c with respect to Earth T =25 yrs

Q: An astronaut exercising on a treadmill maintains a pulse rate of 150 per minute. If he exercises for…

A:

Q: A tuning fork has a frequency of 800 Hz and hence a period of 1.25 × 10 −3 s. If the tuning fork is…

A: The given values are, f=800 HzT=1.25×10-3 sv=0.690c

Q: An astronaut traveling at a speed of 0.75 c requires 25 years,as measured on earth,to make a round…

A:

Q: If relativistic effects are to be less than 3%, then y must be less that 1.03. At what relative…

A:

Q: Suppose that you have found a way to convert the rest energy of any type of matter directly to…

A:

Q: Suppose that you have found a way to convert the rest energy of any type of matter directly to…

A: The volume of the water sufficient to slowly push the moon away from the earth is 5.812 liters.

Q: In the experiment to verify time dilation by flying the cesium clocks around the Earth, what is the…

A: The concept of time dilation explains that the measured interval in a moving system is greater than…

Q: How far from the earth would you be able to travel in a lifetime of 81 years if you were able to…

A: Given, Life-time measured in the earth's frame t0 = 81 years. speed (v) =0.82 c where "c" = speed of…

Q: Recall, from this chapter, that the factor gamma (γ) governs both time dilation and length…

A:

Q: Suppose that you have found a way to convert the rest energy of any type of matter directly to…

A:

Q: Consider a space shuttle traveling at 8 × 103 m/s above the earth. How much time per day is an…

A: Given: velocity 'v' of the space shuttle = 8 x 103 m/s

Q: According to observer O, a blue flash occurs at ?1 = 10.4m when ?1 = 0.124µs and a red flash occurs…

A: Given : x1 = 10.4 m t1 = 0.124µs = 0.124 x 10-6 s x2 = 23.6 m t2 = 0.138µs = 0.138 x 10-6 s

Q: Answering an emergency beacon, Captain Jack leaves the Earth on a rescue mission at 0.60c, arriving…

A: Given data: -  The speed at which Captain Jack leaves the earth is v = 0.60c. The arrival time at…

Q: In a fit of rage, due to a small drop in his approval rating, Homelander throws a baseball into deep…

A: Solution:

Q: If the kinetic energy of a particle is equal to its rest energy then what must be its speed?

A: Given ,        the kinetic energy of a particle equals to its rest energy                speed (v)…

Q: What are the kinetic energy, the rest energy, and the total energy of a 1.0 g particle with a speed…

A: The mass of rhe particle is m=1.0 g×1 kg1000 g=0.001 kg. The speed of the particle is…

Q: Suppose a spacecraft of mass 17000 kg is accelerated to 0.200 c. How much kinetic energy would it…

A: Given:- Mass(m)=17000 kg Velocity (V)=0.20 c Now, The relativistic kinetic energy of the particle.…

Q: An astronaut at rest has a heart rate of 66 beats/min. What will her heart rate be as measured by an…

A:

Q: A light bulb at point x in the frame of reference of O blinks on and off at intervals Δt = t2 − t1.…

A: Formula : t' =γ(t-vxc2) where t is time in rest frame t' is time in relative frame  γ is 11-v2c2…

Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.