A shop owner measures a suitcase kept on a rack to be 50 cm 25 cm 10 cm . A traveller takes this suitcase on a train travelling with a velocity of 0.6c . If the suitcase is oriented with its length parallel to the train's velocity, determine the dimensions measured by an observer on the ground.

Step-by-step solution

The proper dimensions of the suitcase are L₀ = 50 cm , W₀ = 25 cm , and H₀ = 10 cm . The train is moving with a velocity v = 0.6c . Length contraction occurs only along the direction of motion (parallel to the length). The length measured by the observer on the ground is given by: L = L₀ 1 - v^2 c^2 L = 50 1 - (0.6)^2 = 50 1 - 0.36 = 50 0.8 = 40 cm The dimensions perpendicular to the direction of motion remain unchanged. Thus, the width and height are 25 cm and 10 cm respectively. The dimensions measured by the obs