the laboratory measure the velocity of a spaceship moving along the x axis to be
ID: 1900395 • Letter: T
Question
the laboratory measure the velocity of a spaceship moving along the x axis to be +.75c and the velocity of a supernova dust cloud traveling along the x axis with the velocity -.35c approaching the spaceship. the laboratory measure DX length of the dust cloud that the spaceship will have to pass through to be 6.0*10^7 km.1.) with what velocity does the spaceship measure for the dust cloud approaching it?
2.) a typical dust particle has mass equal to 2.3 *10^-12 kg. according to the spaceship, what is the momentum and energy of a typical dust particle that might hit the spaceship?
3.) how much time does the spaceship record for its passage through the dust cloud?
Explanation / Answer
a)
u' = (u - v)/(1-uv/c2) = (-0.35-0.75)/(1-(-0.35*0.75)) = -0.87129 -0.871c
b)
p = mo v = 1/(1-0.87129*0.87129) * 2.3e-12 * 0.87129*3e8 = 0.001225 Kg.m/s
E = mo c^2 = 1/(1-0.87129*0.87129) * 2.3e-12 * 3e8*3e8 = 421787 J
c)
d0 = d' ' = 6e7 * 1/(1-0.35*0.35) = 6.4051e7 Km
d = d0/ = 6.4051e7 * 1/(1-0.87129*0.87129) = 3.14e7 Km
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