3) Bob throws a ball forwards at speed V?. Alice sees his train moving forwards

Question

3) Bob throws a ball forwards at speed V?. Alice sees his train moving forwards with velocity ?c.
a) How fast does Alice see the ball moving in terms of V? and ??
a) How fast does Alice see the ball moving if V? = 0.5c and ? = 0.9?

4) Now Bob throws the ball at right angles to the direction of travel. After time t?, Bob thinks the ball has reached a position (x,y) = (0, y?).
a) Where does Alice think the ball is?
b) What speed will she observe the ball having in the x direction?
c) In the y direction?
d) In total?

5)
a) If the relative velocity of two frames is zero, what form will the Lorentz transforms take?
b) What form will they take if ? is small (i.e. v << c) but non-zero?
c) Why is this important?


6) Bob is travelling with speed ?c in the x direction relative to Alice. Bob thinks his train is 100 light seconds long.
a) How long does Alice think it is?
b) How could they measure this?

Explanation / Answer

3) a) V?B+ B

b) 0.5c + 0.9

(4) a) V?B*t , yB)

b) V?B

c) B - gt

d)??VB2+(B?gt)2

5) a) Eclipse

b) Straight line

c) To simpify situations.

6) a) 56 light seconds

b) By using Newton's Laws of motion

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