A box at rest has the shape of a cube 3.5 m on a side. This box is loaded onto the flat floor of a spaceship and the spaceship then flies past us with a horizontal speed of 0.80 c. What is the volume of the box as we observe it? Express your answer to two significant figures and include the appropriate units.

The volume of the box observed at the given speed is 25.73 m³.

The given parameters;

The edge length of the cube according to the stationary observer is calculated as;

The volume of the cube is calculated as follows;

Thus, the volume of the box observed at the given speed is 25.73 m³.

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Explanation:

Given:

sides of the cube,

speed of the cube with respect to the observer,

Since the relative velocity of the object is relativistic, so there will be a length contraction according to the observer:

where:

observed length of the side along the direction of velocity

is the observed length of the cube edge only in the direction of the velocity due to relativistic effect of length contraction.

So the observed volume will be: