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Question

A spaceship traveling at 0.70c relative to the earth fires a projectile at 0.60c. The velocity of the projectile as measured from the earth is ____ c. The projectile when at rest is roughly shaped like a cylinder with a length of 0.50 m, a diameter of 0.20 m and is made of steel which has a density of 8050 kg/m3. Its rest mass to the nearest kilogram is ____. After being fired, a person on the earth would calculate its density to be ____ x10^ ____ kg/m3.

Answer 1

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"fires a projectile at 0.60c" ? relative to what ?  assuming relative to the spaceship.

big assumption, the projectile is fired away from the observer....

other directions will give different results.

relativistic speed addition

S = (v+u)/(1+vu/c²)

S = (0.7c+0.6c)/(1+0.6•0.7) = 1.3c/(1+0.42) = 0.915c

Cylinder V = πr²h = π(0.1)²0.5 = 0.0157 m³

8050 kg/m³ x  0.0157 m³ = 126 kg

again, the direction is important.

away or towards, they cannot see the length, just the diameter, which is unchanged

at right angles to the observer:

length shortening

L' = L/γ

γ = 1/√(1–(V²/c²)) = 1/√(1–(0.915²)) = 2.48

apparent length 0.5/2.48 = 0.202 m

but they cannot see the diameter, so volume is unknown.