Obviously, we can make rockets to go very fast, but what is a reasonable top spe

Question

Obviously, we can make rockets to go very fast, but what is a reasonable top speed? Assume that a rocket is fired from rest at a space station in deep space, where gravity is negligible. Assume that c = 3.00 × 10^8 m/s.

a.If the rocket ejects gas at a relative speed of 1900 m/s and you want the rocket's speed eventually to be 1.00×103 c, where c is the speed of light, what fraction of the initial mass of the rocket and fuel is not fuel? (ln(m/m0)

b.What is this fraction if the final speed is to be 3700 m/s ? (m/m0)

Explanation / Answer

a )

given

v = 1900 m/sec

vo = 0 m/sec

final speed V = 1.00 X 103 c

C = 3 X 108 m/sec

rocket speed V = 1.00 X 103 X 3 X 108

V = 3 X 105 m/sec

the equation is m / mo = exp ( V / v )

m / mo = exp ( 3 X 105 / 1900 )

m / mo = 3.73 X 1068

b )

m / mo = exp ( - 3700 / 1900 )

m / mo = 0.1426

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.