Answer:
v = 83.1 % of speed of light
Explanation:
given,
T_e is the earth time = 2.7 s
T_s is the ship time = 1.5 s
we know,
[tex]T_s = T_e \times \gamma[/tex]
where c is the speed of light
v is the speed of the rock star moving
[tex]T_s = T_e\times \sqrt{1-\dfrac{v^2}{c^2}}[/tex]
[tex]1.5= 2.7\times \sqrt{1-\dfrac{v^2}{c^2}}[/tex]
[tex] \sqrt{1-\dfrac{v^2}{c^2}} =0.556[/tex]
squaring both side
[tex] 1-\dfrac{v^2}{c^2}=0.3086[/tex]
[tex] v^2=0.6914c^2[/tex]
v = 0.831 c
v = 83.1 % of speed of light
