Question

Quick answer please. THANKS.

A seen from the Earth, the distance from Earth to the Sun is 1.50E 11 meters. A certain particle travels that distance in only 9.62 minutes. What is the speed of the particle (v) as seen from Earth? From the perspective of the particle, how much time (Delta t_p) does is take to reach the Earth? Delta t_p = (note: Specify your answer in minutes.) From the perspective of the particle, what is the distance (Delta L_p) from the Sun to the Earth? Delta L_p =

Answer 1

Part A :

given

d = 1.5 X 10¹¹ m

t = 9.62 minutes

t = 9.62 X 60

t = 577.2 sec

speed of the particle is v = d / t

v = 1.5 X 10¹¹ / 577.2

v = 2.59 X 10⁸ m/s

v = 2.59 X 10⁸ / 3 X 10⁸

v = 0.8633 c

Part B :

$\Delta$ t_p = t / ( $\sqrt{}$ 1 - v² / c² )

v = 0.8633 c

$\Delta$ t_p = 577.2 / ( $\sqrt{}$ 1 - 0.8633² c² / c² )

$\Delta$ t_p = 1143.6696 sec

$\Delta$ t_p = 1143.6696 / 60

$\Delta$ t_p = 19.06 min

Part C :

$\Delta$ L_p = L X ( $\sqrt{}$ 1 - v² / c² )

$\Delta$ L_p = 1.5 X 10¹¹ X ( $\sqrt{}$ 1 - 0.8633² c² / c² )

$\Delta$ L_p = 1.5 X 10¹¹ X 0.504

$\Delta$ L_p = 7.57 X 10¹⁰ m