2. More Harry Potter (sorry) Harry Potter, flying his broomstick at speed 0.6c p

Question

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 travelling 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,

how long (in the stationary frame) after the dragon passed Hermione did she cast her spell?

Explanation / Answer

a. in Harry's frame of reference, the speed of dragon= relative velocity of dragon with respect to Harry = 0.8c - 0.6 c =0.2c

b. The moment dragon reached Hermione, the distance of Harry from Hermione = 0.6c x 10 =6c

speed of dragon with reference to Harry=0.2 c

so time taken = distance/speed = 6 c /0.2 c = 30 s

c. the distance was 6 c

d. As the speed of magic spells are same, both cast them at same time.

so distance travelled by magic spell of harry + distance travelled by magic spell of hermione = 6c

so, relative speed of magic spell by hermione x t + relative speed of magic spell by harry x t=6c

so 0.2c x t + 1.8c x t = 6c

so, 2c x t =6c

so, t= 3s

so after 3s, Hermione cast her spell.

all the best in the course work

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