(i) Two events occur at the same point \( x^{\prime} \) at times \( t_{1}^{\prime} \) and \( t_{2}^{\prime} \) in a frame \( \mathrm{S} \), which moves with speed \( v \) relative to the frame \( \mathrm{S} \). What is the spatial separation of the two events measured in \( \mathrm{S} \) ? (ii) Elephants have a gestation period of 21 months. Suppose a freshly impregnated elephant is placed on a spaceship and sent towards a distant space jungle at a speed \( v=0.75 c \), where \( c \) is the speed of light. If we monitor radio transmission from the space ship, how long after the launch might we expect to hear the first squealing trumpet from the newborn calf? (iii) Sketch the space-time diagram [ ct versus x ] for part (ii) showing the elephant's worldline and the worldline of the radio signal.
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