91影视

At what speed, in $m/s,$would a moving clock lose role="math" localid="1649531760117" $1.0\text{ns}$in $1.0$day according to experimenters on the ground?

Hint: Use the binomial approximation.

You fly $5000km$across the United States on an airliner at $250m/s.$You return two days later at the same speed.

a. Have you aged more or less than your friends at home?

b. By how much?

Hint: Use the binomial approximation

Teenagers Sam and Tom are playing chicken in their rockets. As FIGURE Q36.2 shows, an experimenter on earth sees that each is traveling at $0.95\mathrm{c}$as he approaches the other. Sam fires a laser beam toward Tom.

a. What is the speed of the laser beam relative to Sam?

b. What is the speed of the laser beam relative to Tom?

At $\mathrm{t}=1.0\mathrm{s}$, a firecracker explodes at $\mathrm{x}=10\mathrm{m}$in reference frame S. Four seconds later, a second firecracker explodes at $\mathrm{x}=20\mathrm{m}$. Reference frame S鈥� moves in the x-direction at a speed of $5.0\mathrm{m}/\mathrm{s}$. What are the positions and times of these two events in frame S鈥�?

Jill claims that her new rocket is $100m$long. As she flies past your house, you measure the rocket鈥檚 length and find that it is only $80m$ What is Jill鈥檚 speed, as a fraction of $c$?

A cube has a density of $2000kg/m^3$while at rest in the laboratory. What is the cube鈥檚 density as measured by an experimenter in the laboratory as the cube moves through the laboratory at $90\%$of the speed of light in a direction perpendicular to one of its faces?

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?

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?