91影视

A muon travels $60km$through the atmosphere at a speed of $0.9997c$.According to the muon, how thick is the atmosphere?

Our Milky Way galaxy is $100,000ly$in diameter. A spaceship crossing the galaxy measures the galaxy鈥檚 diameter to be a mere $1.0ly$.

a. What is the spacecraft鈥檚 speed, as a fraction of $c$, relative to the galaxy?

b. How long is the crossing time as measured in the galaxy鈥檚 reference frame?

A human hair is about $50渭m$in diameter. At what speed, in m/s, would a meter stick 鈥渟hrink by a hair鈥�?

Hint: Use the binomial approximation.

A rocket travels in the $x$-direction at speed $0.60c$ with respect to the earth. An experimenter on the rocket observes a collision between two comets and determines that the spacetime coordinates of the collision are $(x^{\text{'}},t^{\text{'}})=(3.0脳{10}^{10}m,200s)$. What are the spacetime coordinates of the collision in earth鈥檚 reference frame?

An event has spacetime coordinates $(x,t)=(1200m,2.0渭s)$in reference frame $S$. What are the event鈥檚 spacetime coordinates (a) in reference frame $S\text{'}$that moves in the positive $x$-direction at $0.80c$and (b) in reference frame $S\text{'}\text{'}$that moves in the negative $x$-direction at$0.80c$?

In the earth鈥檚 reference frame, a tree is at the origin and a pole is at $x=30$km. Lightning strikes both the tree and the pole at $t=10渭s$. The lightning strikes are observed by a rocket traveling in the $x$-direction at $0.50c$.

a. What are the spacetime coordinates for these two events in the rocket鈥檚 reference frame?

b. Are the events simultaneous in the rocket鈥檚 frame? If not, which occurs first?

A rocket cruising past earth at $0.80c$shoots a bullet out the back door, opposite the rocket鈥檚 motion, at $0.90c$ relative to the rocket. What is the bullet鈥檚 speed, as a fraction of $c$, relative to the earth?

A newspaper delivery boy is riding his bicycle down the street at $5.0\mathrm{m}/\mathrm{s}$. He can throw a paper at a speed of $8.0\mathrm{m}/\mathrm{s}$. What

is the paper鈥檚 speed relative to the ground if he throws the paper (a) forward, (b) backward, and (c) to the side?

Firecracker A is $300\mathrm{m}$ from you. Firecracker B is $600\mathrm{m}$ from you in the same direction. You see both explode at the same time. Define event 1 to be 鈥渇irecracker A explodes鈥� and event 2 to be 鈥渇irecracker B explodes.鈥� Does event 1 occur before, after, or at the same time as event 2? Explain.

A distant quasar is found to be moving away from the earth at $0.80c$. A galaxy closer to the earth and along the same line of sight is moving away from us at $0.20c$. What is the recessional speed of the quasar, as a fraction of $c$, as measured by astronomers in the other galaxy?