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Rocket Science: CH 83. A rocket of mass M moving at speed v ejects an infinitesimal mass dm out its exhaust nozzle at speed vex. (a) Show that con- servation of momentum implies that M dy = vex dm, where dy is the change in the rocket's speed. (b) Integrate this equation from some initial speed v; and mass M; to a final speed vf and mass Mf Vf to show that the rocket's final velocity is given by the expression V₁ = V¡ + Vex ln(M¡/M₁).

Rocket Science: CH 83. A rocket of mass M moving at speed v ejects an infinitesimal mass dm out its exhaust nozzle at speed vex. (a) Show that con- servation of momentum implies that M dy = vex dm, where dy is the change in the rocket's speed. (b) Integrate this equation from some initial speed v; and mass M; to a final speed vf and mass Mf Vf to show that the rocket's final velocity is given by the expression V₁ = V¡ + Vex ln(M¡/M₁).

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter9: Linear Momentum And Collisions
Section: Chapter Questions
Problem 78P: A rocket takes off from Earth and reaches a speed of 100 m/s in 10.0 s. If the exhaust speed is 1500...
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Rocket Science: CH 83. A rocket of mass M moving at speed v ejects an infinitesimal mass dm out its exhaust nozzle at speed vex. (a) Show that con- servation of momentum implies that M dy = vex dm, where dy is the change in the rocket's speed. (b) Integrate this equation from some initial speed v; and mass M; to a final speed vf and mass Mf Vf to show that the rocket's final velocity is given by the expression V₁ = V¡ + Vex ln(M¡/M₁).
Transcribed Image Text:Rocket Science: CH 83. A rocket of mass M moving at speed v ejects an infinitesimal mass dm out its exhaust nozzle at speed vex. (a) Show that con- servation of momentum implies that M dy = vex dm, where dy is the change in the rocket's speed. (b) Integrate this equation from some initial speed v; and mass M; to a final speed vf and mass Mf Vf to show that the rocket's final velocity is given by the expression V₁ = V¡ + Vex ln(M¡/M₁).
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