Question

Q5.

1. With the aid of a spacetime diagram illustrate the following terms:
   1. past light cone,            ii. future light cone,            iii. worldline of a relativistic particle.
2. When is a spacetime interval described as:
   1. timelike,          (2 marks) ii. spacelike,            (2 marks) iii. lightlike?            (2 marks)
3. A jet is flying at 900ms−¹ relative to the ground. How much time must elapse before

                         a clock in the jet and one on the ground differ by 2.00s?                                                     (4 marks)

4. How fast must a spacecraft travel relative to the earth for each day on the spacecraft

                        to correspond to 3days on the earth?                                                                                      (4 marks)

5. A certain particle has a lifetime of 2.00×10−⁷s when measured at rest.

How far does the particle go before decaying if its speed is 0.99c?

Answer 1

a) weet s' Pxze Future light Cone cat event-2 I I - 7x 2 Event-1 Past light cone X=-et The space time interval bethween two event is given by (As)2 = (est) ² (one) 2 j) plog region is called past light Cone. 1) glop region is called Future light Cone tet are called world line. b)) ) Time like if ($5)?>0 lie. Ent > 14x| then the interval is called time like ii) Space like (AS) ² <o lie. eat < 10x1 then space time internal Called space like . 10) CS Scanned with CamScanner

3) At = Ji-ur ; to - ta' let , tg=ts=0 The equation of time dialation st' At=tzt st'te'-th Vivre te-tę = t-tz Vi_0% 2 ty-ty'= 25 2 = +2 [ ] - (1 - { v%n)] v<<e binomial ta expansion 4*(3x108) = 4.44x10''se ar, an, 2 2 2 r2 = 놀 를 402 va た 2(بانو) Please give a nating, it will help me doubt sure help don't go eve , Comment any - CS Scanned with CamScanner

* Light like AS=0 ire. cat=kal then it's called light like: Lorento from the equa hion of time dialation At = VI-V77 v=90omis Al' = 2009 At= 2 3 1900 3x108 $) ? d)) 2 &t=3 days At=1 day At = At' V1-0% 3 r2u2/2 1-0% क ver 1- 9 Va 5 % 0.942 C 0.942 C. Velocity of space -craft is e)) 2.00 x 10-7s 0.99€ st 2 x 10-7 = 1.42x10-6 - V-0-99)2 sec Distance Covered verl=0.99x1.42 * 3x108x10-6 = 4.21.74 m CS Scanned with CamScanner
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