Question

In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is 430 ly away, and that you want your 20,000 kg rocket to move so fast that you age only 38 years during the round trip.

a)How fast must the rocket travel relative to earth?

B)How much energy is needed to accelerate the rocket to this speed?

c)The total energy used in the United States in the year 2005 was roughly 1.0 *10^20 J. Compare the rocket's energy to this value by computing the ratio Energy of the rocket/ Energy used by the US.

Answer 1

Step-by-step explanation:

Let the required velocity of rocket be v .

We shall use the formula of time dilation to find the velocity of rocket .

t =
`\frac{t'}{\sqrt{1-(v^2)/(c^2) } }`

t = 430

t' = 38

`430=\frac{38}{\sqrt{1-(v^2)/(c^2) } }`

`\sqrt{1-(v^2)/(c^2) } }=(38)/(430)`

`1-(v^2)/(c^2)` = .0078

`(v^2)/(c^2)` =.9922

`(v)/(c)` = .996

v = .996 x 3 x 10⁸ m /s

= 2.988 x 10⁸ m /s

B )

Kinetic energy of rocket

= 1/2 m v²

= .5 x 20000 x (2.988 x 10⁸ )²

= 8.9 x 10²⁰ J .

C )

This energy is 8.9 times the energy requirement of United states in the year 2005 .