for the 2) quesiton,please help me with proving the coefficient B,i can only fig

Question

for the 2) quesiton,please help me with proving the coefficient B,i can only figure out A,and please also show the whole work of question 3) with full detailed(i can not understand those complex proving method)thank you.

Using the properties of the hyperbolic trig functions, and the fact that tanh (theta) v0/c, show that: A = gamma = 1/ , B/c = v0/c, where A and B are the coefficients we discussed in class. Show that the space-time interval (squared), (Delta s)2, does not remain the same under a Galilean boost. (You can consider just a boost in the x-direction if you want).

Explanation / Answer

under a galilean boost, x->x'+vt, t->t'

(delta s')^2 = x'^2 -t'^2 = (x+vt)^2 - t^2

which is not equal to

(delta s)^2 = x^2 -t^2

hence proved

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