1.

At the two ends of a Quidditch field are goal posts. Harry Potter and Ginny, under a powerful spell, are flying towards each other low to the ground. They are on a fatal collision course, with Harry moving at 0.6c and Ginny at 0.8c. They pass the goalposts at the same time (in the ground’s frame of reference). Standing between them, right in the middle of the field, Hermione anticipates the collision and casts Stupefy at both of them, at the instant in which Harry and Ginny pass over the goalposts. Spells travel at the speed of light.
Does there exist an observer in whose reference frame Harry and Ginny are hit by the Stupefy spell at the same time? if so, what are this observer’s speed and direction relative to the ground (ie, is the observer moving towards Ginny or towards Harry)?

2.

More Harry Potter (sorry) Harry Potter, flying his broomstick at speed 0.6c passes Hermione standing on the ground. Ten seconds (in the ground’s frame of reference) after Harry passes Hermione, a dragon chasing Harry and traveling in the same direction at 0.8c passes Hermione.

(a) How fast is the dragon moving in Harry’s frame of reference?

(b) How long, in Harry’s frame of reference, would it take for the dragon to catch Harry (from the moment when Harry passed Hermione)?

(c) In Harry’s frame of reference, how far was the dragon behind Harry at the instant when Harry passed Hermione?

(d) Sometime after the dragon passes Hermione, but before the dragon catches Harry, Hermione and Harry both cast a Stupefy spell to stun the dragon. Their two spells reach the dragon at exactly the same time. Also, in the dragon’s frame of reference, the two spells were cast at exactly the same time. Assuming that magic spells travel at the speed of light, 1 how long (in the stationary frame) after the dragon passed Hermione did she cast her spell?

Answer rating: 100% (QA)

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