Earth's neighboring galaxy, the andromeda galaxy, is a distance of 2.54×10^7 light-years from earth. if the lifetime of a human is taken to be 70.0 years, a spaceship would need to achieve some minimum speed to deliver a living human being to this galaxy. how close to the speed of light would this minimum speed be?

0.9999986*c

Explanation:

The ship would travel 2.54*10^7 light years, which means that at a speed close to the speed of light the trip would take 2.54*10^7 years from the point of view of an observer on Earth. However from the point of view of a passenger of that ship it will take only 70 years if the speed is close enough to the speed of light.

Where

Δt is the travel time as seen by a passenger

Δt' is the travel time as seen by someone on Earth

v is the speed of the ship

c is the speed of light in vacuum

We can replace the fraction v/c with x

It would need to travel at 0.9999986*c

electrical potential energy =0.072 j

explanation:

electrical potential energy is given by

u= q δv

q= charge=6 c

δv= potential difference and is given by

δv= e d

e= electric field

d= distance=5 mm=0.005 m

δv=2.4 (0.005)=0.012 v

now electric potential energy= u= q δv

u=6 (0.012)

u=0.072 j