Question

1. ralph, who is at rest inside a relativistic train, observes that izah, who is at rest in a train - station, is moving to the right with a speed of 0.400. crissy, who is at rest inside the train, observes that izah is moving to her left with a speed of 0.900. calculate the velocity parameter of izah according to crissy. calculate the speed of izah according to crissy. finally, calculate the speed of the train moving to the left or to the right according to izah, who observes the train moving to be at rest.

Explanation:

Step1: Recall relativistic velocity - addition formula

The relativistic velocity - addition formula is $u=\frac{u'+v}{1 + \frac{u'v}{c^{2}}}$, where $u$ is the velocity of an object as measured in the stationary frame, $u'$ is the velocity of the object in the moving frame, and $v$ is the velocity of the moving frame relative to the stationary frame. Let the stationary frame be the frame of Crissy (at rest), the moving frame be the frame of the train (where Ralph is at rest), $v = 0.400c$ (speed of the train relative to Crissy), and $u'=- 0.900c$ (speed of Izah relative to Ralph).

Step2: Substitute values into the formula

Substitute $u'=-0.900c$ and $v = 0.400c$ into the formula $u=\frac{u'+v}{1+\frac{u'v}{c^{2}}}$. We get $u=\frac{-0.900c + 0.400c}{1+\frac{(-0.900c)\times(0.400c)}{c^{2}}}$. First, simplify the numerator: $-0.900c+0.400c=-0.500c$. Then, simplify the denominator: $1+\frac{(-0.900c)\times(0.400c)}{c^{2}}=1-0.360 = 0.640$.

Step3: Calculate the final velocity

So, $u=\frac{-0.500c}{0.640}\approx - 0.781c$. The negative sign indicates that Izah is moving to the left according to Crissy.

Answer:

Left