b. In Bob's reference frame, how much time is there between when he sees Alice first fire the beam, and when he sees the beam first hit the ground? (Hint: remember to account for the travel time of light to Bob's eyes.)
Given constants:
## Flashlight
Alice the Mad Scientist, travelling in her flying car at height h above the ground, shoots a beam of muons at the ground. Bob, observing from the ground at distance R≫h from Alice's car, decides to check some facts about special relativity. Assume the muons travel extremely close to the speed of light in Alice's frame.
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a. Alice's car flies at horizontal speed v=βc. Alice shoots her muon beam straight down, in her reference frame. Express your answers in terms of β,h,R and fundamental constants.
Context question:
i. What is the horizontal velocity of the muons in Bob's reference frame?
Context answer:
v=βc
Context question:
ii. What is the vertical velocity of the muons in Bob's reference frame?
Context answer:
c1−β2
Context question:
iii. How long does it take the muons to reach the ground in Bob's reference frame?
Context answer:
Δt=c1−β2h