A rocket speeding by the Earth at 0.917c is known,when at rest,to be roughly cylindrical with a radius of 15 m and a length of 150 m.When speeding by,what is its volume,as measured by observers on Earth? A) 6.78 $\times$ 10³ m³ B) 1.70 $\times$ 10⁴ m³ C) 4.24 $\times$ 10⁴ m³ D) 1.35 $\times$ 10⁴ m³ E) 1.06 $\times$ 10⁵ m³

Question

Quizplus · Accepted Answer

To find the volume of the rocket, we need the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height (or length) of the cylinder. 
Since the rocket is traveling at a high speed relative to Earth, we need to use the formula for length contraction: 
L' = L √(1 − v^2/c^2), 
where L is the rest length (150 m), v is the velocity of the rocket (0.917c), and c is the speed of light.
Plugging in the values, we get: 
L' = 150 √(1 − 0.917^2) ≈ 43.32 m
Now we can find the volume of the cylinder: 
V' = π(15)^2(43.32) ≈ 29,300 m^3 
Therefore, the volume of the rocket, as measured by observers on Earth, is approximately 2.93 x 10^4 m^3, which is closest to option C.

A Rocket Speeding by the Earth at 0 ×\times× 103 M3 B) 1

A Rocket Speeding by the Earth at 0 $\times$ 10³ M³
B) 1