Physics, 21.06.2021 17:10 loredobrooke5245

Alice's friends Bob and Charlie are having a race to a distant star 10 light years away. Alice is the race official who stays on Earth, and her friend Darien is stationed on the star where the race ends. Bob is in a rocket that can travel at 0.7c; whereas Charlie's rocket can reach a speed of 0.866c. Bob and Charlie start at the same time. Draw space- diagrams from each perspective. Required:
Estimate how long it takes Bob and Charlie to finish the race from each perspective.

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Answer from: 22katelynfrankouqqrb

Solution :

The distance between the starting point and the end point, L_0 = 10 light years

But due to the relativistic motion of Bob and Charlie, the distance will be reduced following the Lorentz contraction. The contracted length will be different since they are moving with different speeds.

For Bob,

Speed of Bob's rocket with respect to Alice, $L_b = 0.7 \ c$

So the distance appeared to Bob due to the length contraction,

$L_b=L_0\sqrt{1-\frac{V_b^2}{c^2}$

$L_b=10\times \sqrt{1-0.49} \ Ly$

$=7.1 \ Ly$

Therefore, the time required to finish the race by Bob is

$t_b = \frac{L_b}{V_b}$

$=\frac{7.1 \ c}{0.7 \ c}$

= 10.143 year

For Charlie,

Speed of Charlie's rocket with respect to Alice, $L_c = 0.866 \ c$

So the distance appeared to Charlie due to the length contraction,

$L_b=L_0\sqrt{1-\frac{V_c^2}{c^2}$

$L_b=10\times \sqrt{1-0.75} \ Ly$

$=5 \ Ly$

The time required to finish the race by Charlie is

$t_b = \frac{L_c}{V_c}$

$=\frac{5 \ c}{0.866 \ c}$

= 5.77 year

Answer from: Quest

The car would move to the right with 150 n of force. the 150 n of force from friction and air resistance slows the car from moving to the right with 300 n of force.

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

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Alice's friends Bob and Charlie are having a race to a distant star 10 light years away. Alice is th...

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