91Ó°ÊÓ

An experimenter arranges to trigger two flashbulbs simultaneously, producing a big flash located at the origin of his reference frame and a small flash at $\mathbf{3}\mathbf{.}\mathbf{0}\mathit{k}\mathit{m}$. An observer moving at a speed of $\mathbf{0}\mathbf{.}\mathbf{250}\mathit{c}$in the positive direction of $\mathit{x}$also views the flashes. (a) What is the time interval between them according to her? (b) Which flash does she say occurs first?

Bullwinkle in reference frame S^' passes you in reference frame S along the common direction of the x^' and x axes, as in Fig. 37-9. He carries three meter sticks: meter stick 1 is parallel to the x^' axis, meter stick 2 is parallel to the y^' axis, and meter stick 3 is parallel to the z^' axis. On his wristwatch he counts off 15.0 s, which takes 30.0 s according to you. Two events occur during his passage. According to you, event 1 occurs at ${\mathbf{x}}_{\mathbf{1}}\mathbf{=}\mathbf{33}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}$and ${\mathbf{t}}_{\mathbf{1}}\mathbf{=}\mathbf{22}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{ns}$, and event 2 occurs at ${\mathbf{x}}_{\mathbf{2}}\mathbf{=}\mathbf{53}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}$and ${\mathbf{t}}_{\mathbf{2}}\mathbf{=}\mathbf{62}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{ns}$. According to your measurements, what is the length of (a) meter stick 1, (b) meter stick 2, and (c) meter stick 3? According to Bullwinkle, what are (d) the spatial separation and (e) the temporal separation between events 1 and 2, and (f) which event occurs first?

In Fig. 37-9, observer S detects two flashes of light. A big flash occurs at ${\mathbf{x}}_{\mathbf{1}}\mathbf{=}\mathbf{1200}\mathbf{}\mathbf{m}$and, $\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{μ²õ}$later, a small flash occurs at ${\mathbf{x}}_{\mathbf{2}}\mathbf{=}\mathbf{480}\mathbf{}\mathbf{m}$. As detected by observer S^', the two flashes occur at a single coordinate x^'. (a) What is the speed parameter of S^', and (b) is S^' moving in the positive or negative direction of the x axis? To S^', (c) which flash occurs first and (d) what is the time interval between the flashes?

Stellar system Q₁ moves away from us at a speed of 0.800c. Stellar system Q₂, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q₂ as measured by an observer in the reference frame of Q₁?

A spaceship whose rest length is 350 m has a speed of 0.82c with respect to a certain reference frame. A micrometeorite, also with a speed of 0.82c in this frame, passes the spaceship on an antiparallel track. How long does it take this object to pass the ship as measured on the ship?

A spaceship, moving away from Earth at a speed of 0.900c, reports back by transmitting at a frequency (measured in the spaceship frame) of 100 MHz. To what frequency must Earth receivers be tuned to receive the report?

Certain wavelengths in the light from a galaxy in the constellation Virgo are observed to be 0.4% longer than the corresponding light from Earth sources. (a) What is the radial speed of this galaxy with respect to Earth? (b) Is the galaxy approaching or receding from Earth?

A spaceship is moving away from Earth at speed 0.20c. A source on the rear of the ship emits light at wavelength 450 nm according to someone on the ship. What (a) wavelength and (b) color (blue, green, yellow, or red) are detected by someone on Earth watching the ship?

How much work must be done to increase the speed of an electron (a) from 0.18c to 0.19c and (b) from 0.98c to 0.99c? Note that the speed increase is 0.01c in both cases.

(Come) back to the future. Suppose that a father is 20.00 y older than his daughter. He wants to travel outward from Earth for 2.000 y and then back for another 2.000 y (both intervals as he measures them) such that he is then 20.00 y younger than his daughter. What constant speed parameter $\mathit{β}$ (relative to Earth) is required?