a) Given a = (7, −6, 4) and b = (3, 8, −1), find a ·b and a ×b. b) A (100 m) long spaceship is travelling at 90% the speed of light. How long is the spaceship as measured by a stationary observer?
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a) Given a = (7, −6, 4) and b = (3, 8, −1), find a ·b and a ×b.
b) A (100 m) long spaceship is travelling at 90% the
by a stationary observer?
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- An electron has total energy 2.50 MeV. Find (a) its kinetic energy and (b) its speed.A particle has a rest mass of 7.15×10−27 kg and a momentum of 5.75×10−18 kg·m/s. Determine the total relativistic energy ? of the particle. ?= J Find the ratio of the particle's relativistic kinetic energy ? to its rest energy ?rest. ??rest=A particle has γ=18,399. a) Calculate c-v in m/s. (I would have asked for 1 - v/c, making the answer dimensionless, but the system doesn't seem to take numbers that small. Gamma is chosen to make the particle extremely close to the speed of light.) If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 1,739 MeV/c, calculate its energy in MeV. Thank you so much!!
- A particle detector can be used to measure the speed of an unstable particle if the lifetime is known. Particle 'X' has mean lifetime 7 in its rest frame. Suppose 'X' particles are created in an experiment inside the detector by a nuclear reaction. If the 'X' particles leave tracks with mean length L before they decay into other particles, what is the mean speed of the 'X' particles? Express the answer in terms of the speed of light. T = 282.0 ps; L= 10.5 cm;A spacecraft is traveling at ~v = 38.4km s (yes, that is a reasonable speed for a rocket). How long will it take to travel from the earth to the moon, a distance of 384 Mm from Earth?A spaceship travels at a speed of 2.4 x 108 m/s. A clock in the spaceship passes 60 seconds. How much time (in second) passes on the clock at rest on the ground?
- Figure 6 m/s 3 m/s 2 1 Part E What is the speed of ball 1 in a referece frame that moves with ball 2? V₁ = 跖 ΜΕ ΑΣΦ Submit Request Answer Part F ? m/s What is the direction of ball 1 in a referece frame that moves with ball 2? left O right ○ the ball is at rest Submit Request Answer Part G Complete previous part(s) Part H Complete previous part(s) Provide FeedbackA particle has a rest mass of 7.15×10−27 kg and a momentum of 5.56×10−18 kg·m/s. Determine the total relativistic energy E of the particle. Find the ratio of the particle's relativistic kinetic energy K to its rest energy ?rest.Earth's neighboring galaxy, the Andromeda Galaxy, is a distance of 2.54 × 107 light-years from Earth. If the lifetime of a human is taken to be 85.0 years, a spaceship would need to achieve some minimum speed Umin to deliver a living human being to this galaxy. How close to the speed of light would this minimum speed be? Express your answer as the difference between Umin and the speed of light c. C- Umin = m/s
- In special relativity, we introduced the momentum of a particle in a given Lorentz frame as pu = (E, pi ), where E is the energy of the particle and pi is the relativistic 3-momentum. Explain why, in general relativity, the energy of a particle measured by an observer is given, irrespective of the coordinate system used, by −p · uobs, where pu is the momentum of the particle and uuobs is the velocity of the observer in those coordinates.a) Suppose you decide to travel to a star 66 light-years away at a speed that tells you the distance is only 24 light-years. How many years would it take you to make the trip? Express your answer using two significant figures. b)In its own reference frame, a box has the shape of a cube 1.5 mm on a side. This box is loaded onto the flat floor of a spaceship and the spaceship then flies past us with a horizontal speed of 0.90 cc.What is the volume (m3 ) of the box as we observe it?A cylindrical spaceship of length 35.0 m and diameter 8.35 m is traveling in the direction of its cylindrical axis (length). It passes by the Earth at a relative speed of 2.44××1088 m/s. a) What is the length of the ship, as measured by an Earth observer? b) What is the diameter of the ship, as measured by an Earth observer? c) How long does it take the spaceship to travel a distance of 10.0 km according to the ship's pilot? d) How long does it take the spaceship to travel a distance of 10.0 km according to an Earth-based observer?