Three space ships are seen flying past your classroom on a space station. When m

Question

Three space ships are seen flying past your classroom on a space station. When moving, Ship 1 is measured to be only 78% of its length compared to when it is at rest at the space station. Ship 2 is moving away from the space station at 0.6c and Ship 3 is moving toward the space station (in the opposite direction as Ship 2) at 0.8c.

How fast is Ship 1 moving relative to the space station?

a) 0c

            b) 0.23c

            c) 0.43c

            d) 0.63c

            e) 0.83c

After 3 hours pass on your watch, how much time do measure to have passed on Ship 2’s clocks?

a) 1.80 hours

            b) 2.40 hours

            c) 3.00 hours

            d) 3.75 hours

e) 5.00 hours

How fast does Ship 2 measure Ship 3 to be moving?

a) 0.20c

            b) 0.38c

            c) 0.95c

            d) 1.00c

            e) 1.40c

You send a radio signal (at the speed of light) to Ship 3. How fast does Ship 3 measure it approaching?

a) 0.2c

            b) 0.8c

            c) 1.0c

Explanation / Answer

1) option d (0.63c )is the correct answer.

This could only be found by using length contrraction formula. we know that

L = Lo ( 1- V2 / c2)1/2

   Here L0 = 78% of L

     0.78Lo =Lo ( 1-V2 / c2)1/2

0.78 = (1- V2 / c2)1/2

0.6084=1 - V2 / c2

-0.3916 = - V2 / c2

      0.6257 c = V

or V = 0.63 C ( After rounding off)

2) option b ( 2.40) hours is the correct option

Using the formula of time dialation we can find the correct answer. We know that

t = to / (1- v2 / c2)1/2

3hours = to / (1- (0.8c)2 / c2   )1/2

3h= to / (1-0.36 )1/2

3h= to / 0.8

to = 2.4hour (Answer)

3) option c ( 0.95c) is the correct option

Using the formula

Speed of ship 3 measure by ship 2 = u + v / 1+ uV / c2 = 0.8c + 0.6c / 1+ 0.48

= 0.9495 c

This is almost equal to 0.95c

4) option c ( 1c) is the correct option

You can solve this problem by using several techniques but the answer will be speed of light c. The most prominent technique to get insight to this problem is theory of special relativity . According to this theory " The speed of light is a univeral constant." Its mean that radio singal is a light and where ever if you are measuring the speed of light you will get the same value for c. Due to speed of light as a universao constant you ship 3 will measure the value as 1c.

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