Physics · The frame of reference, motion in a straight line, speed and velocity
A train of length is moving in a hilly region. At what speed must it approach a
A train of length \( 100 m \) is moving in a hilly region. At what speed must it approach a tunnel of length \( 80 m \) so that a person at rest with respect to the tunnel will see that the entire train is in the tunnel at one time?
- A. \( 1.25 c \)
- B. \( 0.8 c \)
- C. \( 0.64 c \)
- D. \( 0.6 c \) E \( .0 .36 c \)
Step-by-step solution
The train's proper length is 100 m. Due to length contraction, the tunnel observer sees the train's length as L = L0 * sqrt(1 - v^2/c^2). For the entire train to fit inside the 80 m tunnel, we need L <= 80 m. Setting L = 80 m gives sqrt(1 - v^2/c^2) = 0.8, so 1 - v^2/c^2 = 0.64, v^2/c^2 = 0.36, hence v = 0.6c.
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