How fast would a rocket have to move past a ground observer if the latter were to observe a 3.0% length shrinkage in the rocket length? (c = 3.00 × 10⁸ m/s) A) 1.2 × 10⁸ m/s B) 0.60 × 10⁸ m/s C) 0.73 × 10⁸ m/s D) 0.12 × 10⁸ m/s

Question

Quizplus · Accepted Answer

The length contraction formula is: 
L' = L√(1 - (v^2/c^2))
Where L is the original length, L' is the contracted length, v is the velocity of the rocket relative to the ground observer, and c is the speed of light.

Plugging in the given values, we get:
0.97L = L√(1 - (v^2/c^2))

Simplifying, we get:
0.03 = √(1 - (v^2/c^2))

Squaring both sides, we get:
0.0009 = 1 - (v^2/c^2)
v^2/c^2 = 0.9991

Taking the square root and multiplying by c, we get:
v = 0.73 × 10^8 m/s or 0.73c

Therefore, the answer is choice C.

How Fast Would a Rocket Have to Move Past a Ground