Question

A super train (proper length, 1200 [ft]) travels at a speed of 0.99 [c] as it passes through a tunnel (proper length, 50.0 [ft]). As seen by a trackside observer if the train ever completely within the tunnel?

Answer 1

the super train is not completely within the tunnel.

Step-by-step explanation:

From the given information:

The proper length
`L_o` = 1200 ft

The super train speed = 0.99c

By applying the concept of length contraction, the contracted length of the super-train can be determined by using the formula:

`L = L_o \sqrt{1-(v^2)/(c^2)}`

`L = 1200 \sqrt{1-((0.99c)^2)/(c^2)}`

`L = 1200 √(1-(0.99)^2)`

`L = 1200 √(1-0.9801)`

`L = 1200 √(0.0199)`

L = 169.3 ft

≅ 169 ft

Thus, the contracted length is 169 ft more than the proper length of the tunnel L' 50 ft.

As such, the super train is not completely within the tunnel.