Question

A rocket of mass m is fired vertically upward and after the fuel burning it weighs m'. Ejection of fuel gas is at a constant rate of m₀per second with a constant velocity of u_rel relative to the rocket. Final speed of rocket after the complete burn out of fuel is given by v =

• A. u_rel log_e$\frac { \mathrm { m } } { \mathrm { m } ^ { \prime } }$
• B. u_rel log_e$\frac { \mathrm { m } _ { 0 } } { \mathrm {~m} }$
• C.
  • u_rellog_e
• D. – u_rel

Answer 1

Answer: (A)

u_rel log_e$\frac { \mathrm { m } } { \mathrm { m } ^ { \prime } }$

Answer 2

or $\frac { \mathrm { mdv } } { \mathrm { dt } } = - \mathrm { u } _ { \mathrm { rel } } \frac { \mathrm { dm } } { \mathrm { dt } }$

i.e., dv =

i.e., v = - u_rel= u_rel log_e