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Alex Ar [27]
3 years ago
10

Twin A makes a one way trip at 0.6c to a star 12 light years away while twin B stays on Earth. Each twin sends the other a signa

l once a year by his own time. (a) How many signals does A send during the trip
Physics
1 answer:
hram777 [196]3 years ago
7 0

Answer:

8 signals received by twin A during the trip.

Explanation:

Given that,

Distance = 12 light year

Speed = 0.6 c

Time = 1 year

We need to calculate the time by A

Using formula of time

T=t\sqrt{\dfrac{1+\dfrac{v}{c}}{1-\dfrac{v}{c}}}

Put the value into the formula

T=1\sqrt{\dfrac{1+0.6}{1-0.6}}

T=2\ years

Similarly,

The expression for distance cover by A

D=d\sqrt{1-\dfrac{v^2}{c^2}}

D=12\sqrt{1-(0.6)^2}

D=9.6\ ly

We need to calculate the time

Using formula of time

t=\dfrac{D}{v}

t=\dfrac{9.6}{0.6}

t=16\ years

We need to calculate the signals received by twin A

Using formula for number of signals

n=\dfrac{t}{T}

Put the value into the formula

n=\dfrac{16}{2}

n=8\ signals

Hence, 8 signals received by twin A during the trip.

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Applying logarithm on both sides,

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Applying logarithm on both sides,

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⇒log(4)=\frac{t}{\frac{L}{R}}

⇒t=log4\frac{L}{R}

now subs. \frac{L}{R}=\frac{2}{log2}

⇒t=log4\frac{2}{log2}

also log4=log2^{2}=2log2

⇒t=2log2\frac{2}{log2}

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